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Talk:The Legend of Zelda: Link's Awakening (2019 video game)/Controls

Import?
Thanks for the assist User:2005-Fan!

I just want to make sure I get attribution right for the about page, this was imported from Strategy Wiki, correct? --Mbrickn (discuss • contribs) 22:52, 8 July 2021 (UTC)

D'oh!
When I responded in this Talk:The Legend of Zelda: Link's Awakening/Controls page, I kind of forgot that most of the chapter Wake up! is dedicated to covering controls already, and is a bit more comprehensive then this. I probably should have made that clear in the TOC. However a quick table like this might still be useful to the reader, especially as it's own page for quick look ups. --Mbrickn (discuss • contribs) 23:01, 8 July 2021 (UTC)

 * Yeah this is a basic control reference. It shouldn't hurt to have it. 2005-Fan (discuss • contribs) 23:07, 8 July 2021 (UTC)
 * Cool! This is a dumb question, but is it possible to reimport this from strategywiki with the page history intact? That should help with attribution. I can clean up the missing images. Thanks! --Mbrickn (discuss • contribs) 23:10, 8 July 2021 (UTC)
 * I think said it's okay to attribute in the edit summary. 2005-Fan (discuss • contribs) 23:11, 8 July 2021 (UTC)
 * Cool! Will do --Mbrickn (discuss • contribs) 23:31, 8 July 2021 (UTC)
 * Just to confirm, this was an import, yes? --Mbrickn (discuss • contribs) 23:32, 8 July 2021 (UTC)
 * Yeah, although this was split from the The Legend of Zelda: Link's Awakening/Controls, which was imported. 2005-Fan (discuss • contribs) 23:33, 8 July 2021 (UTC)
 * Yes: https://strategywiki.org/wiki/The_Legend_of_Zelda:_Link%27s_Awakening/Controls 2005-Fan (discuss • contribs) 23:38, 8 July 2021 (UTC)
 * Cool! Thanks for the confirmation! --Mbrickn (discuss • contribs) 00:02, 9 July 2021 (UTC)
 * It's possible to reimport from strategywiki - you can simply merge the page histories in that case (2005-Fan can do it for you). Leaderboard (discuss • contribs) 08:20, 9 July 2021 (UTC)


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The Legend of Zelda: Link's Awakening (2019 video game)/Ancient Ruins Exploration

Crossing the river
Just south of the secret seashell manor is a gap in the river that looks like Link could dash jump across it. Unfortunately, Link can not dash jump across this gap as a stump prevents him from building up enough momentum. Fortunately there is an alternative route. Cut down a bush near the gap to unveil a set of hidden stairs.

Descend down the stairs to find a small partially flooded passageway that goes under the river. Most of the water here is puddle deep, though still deep enough to house shark like monsters. Hug the norther wall and go east to progress. Keep Link's shield raised and stop as the shark monsters approach to safely progress in these tight quarters. Those in a hurry, such as speed runners, may simply run foreword, though they will be almost certain to take some damage in the process.

The exterior ruins
From the stairwell exit, head north and go east along the narrow path obscured by the wall. The owl will visit Link and inform him of two shrines. One shrine is to the north. However the owl wants Link to go to the other shrine to the south first, where there is information regarding the Wind Fish in the ancient ruins.

Continue east and ignore the maze to the north for now. Instead go through the narrow crevice in the southern wall to enter the ancient ruins. This old location is dotted with columns, statues and monsters.

Not all statues are harmless, some will come to life when Link touches them and attack! These mono-eyed states carry neigh impregnable rectangular shields. While it may be tempting to avoid activating hostile statues, it is quite necessary to progress in a few instances where they block the sole path foreword. However their sluggish movements can be easily dodged or walked around most of the time, so there is little danger in deliberately luring them away and then running past, raising the shield to ensure safety if in tight quarters. Eventually Link will make it to the dungeon entrance.

Armored Boss
Just as the first chamber of key dungeon contained pots with bombs, the first chamber of the ancient ruins contains twin pots containing arrows. Take some time to resupply if needed. Head into the northern chamber to be immediately greeted by a mini boss! This huge monster is clad in blue armor, and jumps to slam the ground with it's enormous might, stunning Link if he is touching the ground. Use the Roc's feather to avoid touching the ground and thus avoid being stunned. Jump around the boss with Roc's feather to find an opening, then let loose an arrow to strike it. As the armor of the boss degrades with every strike, it seemingly speeds up. With a few strikes the boss goes down, dropping the Face Key in the process. Pick it up and enter the northern door.

The Relief
The dark room Link enters can be lit through ignoring the twin torches with magic powder. This reveals a large relief on the wall. The main subject of the mural is the Wind Fish, though the owl can be seen in the upper left hand corner. Reading the inscription in the upper right, Link receives a shocking revelation, that the island of Koholint is an illusion, including all it's inhabitants and natural features. HUMAN, MONSTER, SEA, SKY... A SCENE ON THE LID OF A SLEEPER'S EYE... Furthermore, once the dreamer is awakened, the illusion will be dispelled. The author of the relief wishes for the castaway to understand the truth of the situation as the inscription ends.

Leave the ruin interior to be greeted by the owl, who clarifies that the words of the relief are uncertain, and that the only way to know for sure is to confront the Wind Fish. The owl also states that the relief mentions that the dream is from the Wind Fish, but this again is an uncertain claim. The owl also claims it is impossible to tell if one is dreaming until one has awoken. Still tow owl assures Link that the answer will be found, before it once again flies off to the east.

Leave the ruin exterior and head north to find a statue with a disturbing message, poetically claiming that when the Wind Fish sleeps for an extended period of time, the life of the Hero will be placed in jeopardy.

Optional Fairy Fountain
Head into the rocky maze, and head northwest. Bomb the cracked wall at the northwest corner to reveal a cave with a fairy fountain to heal up and replenish fairy bottles.

Questions to consider

 * How does the author of an ancient inscription know that a castaway would read it?
 * Who is the sleeper?
 * Is it really impossible to tell if you are dreaming while asleep? With Lucid Dreaming it's possible, but was the Owl referring to a lucid dream?


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Template:LoZOoT Enemy

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Template:LoZOoT Enemy/doc

Enemy template for The Legend of Zelda: Ocarina of Time. This is used to create a single row for an enemy on the The Legend of Zelda: Ocarina of Time/Enemies page.

Images should be uploaded as "LoZ OoT enemy .png"

Usage:
 * name
 * hp: number of "HP" (basic strikes from Kokiri Sword or Master Sword)
 * damage: Damage dealt (moves can be listed here).
 * first: location first seen in (the first place in our walkthrough).
 * location: dungeons or regions where the monster is found.
 * navi: Navi's description (a quote).
 * notes: miscellaneous notes and strategies to defeat the monster.

Optional, unnumbered parameters:
 * image: specify an alternate filename; exclude "file:" in the syntax.
 * imageparameters: adjust the parameters for the default image or image specified with the image parameter; default size is 100px.
 * image2: second image, if both art and a model is available.

Example

 * Code

 * Output

title: Template:LoZOoT Enemy/doc


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South Park: The Stick of Truth/Gain New Allies

Cartman informs you that the elves have stolen the stick, and instructs you to recruit the Goth kids to help retake it. This quest has three parts.

Recruit the Goth Kids
Go to the school, and make your way around back to find the Goth kids. They will agree to help you only if you act and dress like them.

Noncomformist
Go to Tweek Bros. Coffee and purchase a Dark Roast. On your way out, you will be ambushed by several elves. Don't bother fighting them, as you will gain no experience from the battle, and one of the elves will knock you unconscious after you win. Instead, travel with them to the Elven Kingdom, where Kyle will advise you to join them against Cartman. Afterwards, make your way to Jimbo's Guns, where you will be attacked by a group of sixth graders. Defeat them, and they'll drop cigarettes.

Finally, head to the U-Store It next to Tweek Bros. and purchase goth clothes from the homeless man. Return to the Goth kids afterwards.

PTA Problems
The Goth Kids have one final task: take a picture during the PTA meeting holding a sign that reads "Fuck the Conformists". Head next door to the community center, where the PTA meeting will be in progress. Once the meeting ends, head into the bathroom and Randy will teach you a new magic fart, the Sneaky Squeaker. Test it on Mr. Mackey. Then make your way to where the UFO crashed by the mall. Use the Sneaky Squeaker to distract the guards, then make your way through the gate.

Use the switch by the truck to electrify the puddle of water, then lure the soldier into the puddle to take him out. Use your anal probe to teleport to the top of the building, then smash through the air vent to enter. Defeat the Nazi zombie after the cutscene, then grab the recording device from the table. Make sure to shoot the Chinpokomon off the filing cabinet, as this will be your only chance to collect it.

Head back outside and make your way back to the PTA meeting. From this point on the streets of South Park will be overrun by Nazi zombies, so take extra care to avoid the,. Give the recording to the PTA members, then make your way back to the Goths. Play the Dance Dance Revolution-style minigame to prove you can dance like a goth. Now you must make a decision: Cartman and the Humans, or Kyle and the Elves. Whichever side you choose to join, head back to their respective headquarters and talk to them to continue. Once you have made your decision, climb up the kingdom's tower to summon your fighters.


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The Legend of Zelda: Link's Awakening (2019 video game)/Exploring Animal Village

Finding Animal Village
Head back the stairs used to cross the river, but do not descend down them. Instead head south to find the Animal Village. If you reach the telephone booth, you've gone too far and should return north.

Animal Village
Animal Village is the quirky "Sister City" of Mabe Village. The inhabitants here are not human, but are still friendly to Link.

In the Animal Village, talk to the snow white rabbit near the entrance. This rabbit wants a song from Marin.

In the northwestern house a white rabbit inside will mention a way to the south, which is said to be blocked by a walrus.

The next building to the east houses the crocodile (Or is it an Alligator?) artist Schule Donavitch, as well as a hippo model. Schule Donavitch mentions he made the mermaid statue at Martha's Bay as his unfinished masterpiece. The Hippo Model is less talkative.

The next eastern neighbor is the goat Christine. Concerned with etiquette, she wants flowers. Specifically she wants a pink hibiscus before she will talk to Link. Her house shares a leitmotif with Mr. Write.

The neighboring house to the east is... empty? Looks can be deceiving, but leave for now.

The rabbit in the southeast corner is concerned for Marin, since the monsters have stopped visits between the two villages.

Enter the house in the southeast to meet Chef Bear. Chef Bear wants Link's Honeycomb, and is willing to trade in exchange for a Pineapple. Chef Bear tells Link to fetch Marin to get the walrus blocking the way to move. Chef Bear may also mention their plans to open a Mabe Village branch.

Head to the very south of Animal Village to activate a convenient warp pedestal. Warp back to the Ukuku Prairie to get a shortcut to Mabe Village.

Questions

 * What is good etiquette?

 * What leads to a city having a sister city?


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User:Brienna.Hall77

Hi, I'm a Materials Science student working solely on the Electronic Properties of Materials WikiBook.

title: User:Brienna.Hall77


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Nimrod Programming/Installing Nimrod

As nim is a compiled language, we of course need the compiler on the system that we are on , so lets install it .now the installation procedure depends on your system.

https://nim-lang.org/install.html

and if you want to compile from source then after downloading the source tarball

title: Nimrod Programming/Installing Nimrod


text:
Solutions To Mathematics Textbooks/Algebra (9780132413770)/Chapter 3

Exercise 1.2
Using an "educated guess" one observes that $$5^{p-1} \equiv_p 1$$. With this, it is easy to see that $$5^{-1} \equiv_7 3$$, $$5^{-1} \equiv_{11} 9$$, $$5^{-1} \equiv_{13} 8$$ and $$5^{-1} \equiv_{17} 7$$.

Exercise 1.3
$$(x^3 + 3x^2+3x+1)(x^4 + 4x^3 + 6x^2 + 4x + 1) = x^7 + 7 x^6 + 21 x^5 + 35 x^4 + 35 x^3 + 21 x^2 + 7 x + 1 \equiv_7 x^7 + 1$$, as all the coefficients divisible by 7 reduce to 0.

Exercise 1.10
Let us denote the matrices (appearing in the same order as in the book) by $$0, 1, A, B$$. We need to check the following:

 * $$0, 1, A, B$$ is a group with matrix addition and $$0$$ as the identity. We get the following addition table

So we see that the elements with addition form an abelian group with $$0$$ as the identity.
 * $$1, A, B$$ is a group with $$1$$ as the identity. Again we have the multiplication table
 * $$1, A, B$$ is a group with $$1$$ as the identity. Again we have the multiplication table
 * $$1, A, B$$ is a group with $$1$$ as the identity. Again we have the multiplication table

Again, we see that the elements with matrix multiplication form an abelian group with $$1$$ as the identity.

 * The distributive law follows from the distributive law for matrices in general.

Exercise 1.11
Writing out a product and sum of two elements from the given set, and noticing that the coefficients of both elements, and thus their sums and products are in $$\mathbb{F}_3$$, implies that the sum and product are in the set. To see that each non-zero element has an inverse in the $$+$$ -operation is trivial. To see the same for the product operation, write the equations coming from the condition $$zz^{-1} = 1$$, where $$z$$ is a known element from the set and $$z^{-1}$$ a candidate for its inverse with unknown coefficients as a linear system. By Corollary 3.2.8 this system has a solution. The distribution law is immediate.

Exercise 2.2
a) The space of symmetric matrices is a vector space, since the sum of two symmetric matrices is a symmetric matrix, and a scaling of a symmetric matrix by a scalar is symmetric.

b) The space of invertible matrices is not a vector space, since it does not contain the zero matrix.

c) The space of upper triangular matrices is also a vector space by similar reasoning as used in part a).

Exercise 3.1
One possible basis for the space of symmetric matrices is for example the matrices $$A_{ij}$$ for $$i = 1, \ldots, n,~ j \leq i$$ that have zeros everywhere but in the $$i,j$$ and $$j, i$$ entry. There are $$\binom{n}{2}$$ such matrices, and they are linearly independent, since no two such matrices have ones in the same entry. Furthermore, the matrices $$A_{ij}$$ are symmetric and clearly any symmetric matrix can be written as a linear combination of $$A_{ij}$$.

Exercise 3.7
Let $$c_{ij} \in \mathbb{R}$$ be coefficients such that

$$\sum_{i, j} c_{ij} X_iY_j^t = 0$$. (1)

The matrix $$\sum_{i, j} c_{ij} X_iY_j^t$$ has as the $$k$$th column the vector $$\sum_{i, j} c_{ij}Y_{jk} X_i = \sum_i \left(\sum_j c_{ij}Y_{jk} \right) X_i$$ where $$Y_{jk}$$is the $$k$$th element of the vector $$Y_j$$. Denote $$\alpha_i = \sum_j c_{ij}Y_{jk}$$, so that the (1) implies together with the condition that the vectors $$X_i$$ form a basis that $$\alpha_i = 0$$ for all $$i$$. So then we must have $$\sum_j c_{ij}Y_{jk} = 0$$ for all $$k, i$$. This implies that $$\sum_j c_{ij}Y_j = 0$$ for all $$i$$, but since the vectors $$Y_j$$ form a basis, we must have $$c_{ij} = 0$$ for all $$i$$.

Exercise 3.8
Let $$A$$ be the matrix with the vectors $$v_1, \ldots, v_n$$ as column vectors. Let $$X, B \in F^n$$. Then $$AX = B$$ is equivalent to saying that $$B$$ is a linear combination of the vectors $$v_1, \ldots, v_n$$. By Theorem 1.2.21, $$AX = B$$ has a unique solution $$X$$ if and only if $$A$$ is invertible.

In particular, this means that also $$AX = 0$$ has a unique solution $$X = (0, \ldots, 0)$$. This shows that 1) $$v_1, \ldots, v_n$$ span the space $$F^n$$ and 2) $$v_1, \ldots, v_n$$ are linearly independent.

Exercise 4.2
a) $$\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$.

b) $$\begin{pmatrix} 0 & \cdots & 0 & 1 \\ 0 & \cdots & 1 & 0 \\ \vdots & \vdots & \vdots & \vdots  \\ 1 & 0 &  \cdots & 0 \end{pmatrix}$$.

c) $$\begin{pmatrix} 1 & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} \end{pmatrix}$$ or $$\begin{pmatrix} 1 & -\frac{1}{2} \\ 0 & -\frac{\sqrt{3}}{2} \end{pmatrix}$$.

Exercise 4.3
The given operations correspond to row operations on matrices. By Theorem 1.2.16, any matrix that is invertible can be reduced to the identity using such operations. In Exercise 3.8 we proved that the columns of a matrix form a basis if and only if the matrix is invertible.

Exercise 4.4
a) Any basis in $$V$$ corresponds to a matrix that is invertible, i.e., an element of $$GL_2(\mathbb{F}_p)$$. On the other hand the column vectors of any element from $$GL_2(\mathbb{F})$$ form basis vectors for $$V$$.

b) For $$GL_2(\mathbb{F}_p)$$ we have that there are in total $$p^4$$ matrices in $$\mathbb{F}_p^{2 \times 2}$$ of which we have to count the ones that are not invertible. Considering the columns of a matrix in $$\mathbb{F}_p^{2 \times 2}$$, we have

 * $$p^2-1$$ first columns that are not the $$(0, 0)^t$$ column vector, and $$p-1$$ scalings of the first column with a value other than zero.
 * If the first column is $$(0, 0)^t$$, the second column can be chosen in $$p^2-1$$ ways such that it is not also the $$(0, 0)^t$$ vector.
 * If the second column is $$(0, 0)^t$$, the first column can also be chosen in $$p^2-1$$ ways such that it is not the $$(0, 0)^t$$ vector.
 * There is exactly one matrix with both columns $$(0, 0)^t$$.

Combining these facts, we get that there are $$p^4 - (p^2-1)(p-1) - (p^2-1) - (p^2-1) - 1 = p(p+1)(p-1)^2$$invertible matrices in $$\mathbb{F}_p^{2 \times 2}$$.

For $$SL_2(\mathbb{F}_p)$$ we want to compute the number of matrices in $$\mathbb{F}_p^{2 \times 2}$$ with determinant equal to 1. In $$GL_2(\mathbb{F}_p)$$ there are equally many elements with determinant 1, 2, 3, etc.Therefore, the number of elements in $$GL_2(\mathbb{F}_p)$$ is the number of elements with determinant 1 times $$p-1$$. From the previous calculation we thus get that the number of elements in $$SL_2(\mathbb{F}_p)$$ is $$p(p+1)(p-1)$$.

Exercise 4.5
a) The key for finding the number of subspaces is to find the number of linearly independent vectors in $$\mathbb{F}_p^3$$.

b) The case of $$\mathbb{F}_p^4$$ can be generalised from the previous case:
 * Subspaces of dimension 0: 1.
 * Subspaces of dimension 1: Each subspace is spanned by a nonzero vector of the form $$(a, b, c)^t$$ with $$a,b,c \in \mathbb{F}_p$$. There are $$p^3-1$$ such vectors. For any such given vector, there are $$p-1$$ nonzero scalings with a scalar in $$\mathbb{F}_p$$. Hence, the number of linearly independent vectors is $$(p^3-1)/(p-1) = p^2 + p + 1$$. Each such vector spans a subspace that is different from the subspaces spanned by the others.
 * Subspaces of dimension 2: Let $$W$$ be some maximal collection of linearly independent vectors of $$\mathbb{F}_p^3$$. We know that $$|W| = p^2 + p + 1$$, and any two vectors from $$W$$ span a two-dimensional subspace of $$\mathbb{F}_p^3$$. We can choose two vectors from $$W$$ in $$\binom{p^2 + p + 1}{2}$$ ways, but this is not the number of two-dimensional subspaces of $$\mathbb{F}_p^3$$. Indeed, say we choose $$v_1, v_2 \in W$$ such that $$v_1 \neq v_2$$. Then $$V = \textrm{Span}(v_1, v_2)$$ is a subspace of $$\mathbb{F}_p^3$$ containing $$p^2$$ points and $$p^2 / (p-1) = p + 1$$ linearly independent vectors. As $$p > 1$$, this means $$V$$ contains some vector $$w \in W, w \neq v_1, v_2$$. The number of pairs of linearly independent vectors in $$V$$ is $$\binom{p + 1}{2}$$, and hence the number of two-dimensional subspaces of $$\mathbb{F}_p^3$$ is $$\binom{p^2 + p + 1}{2} / \binom{p+1}{2} = p^2 + p + 1 $$. Another way to arriving the same conclusion is as follows: Let $$V$$ be a subspace of $$\mathbb{F}_p^3$$ of dimension 2. Then, $$V$$ is spanned by two linearly independent vectors, and there is a vector $$v \in \mathbb{F}_p^3$$ such that $$v \notin V$$. In other words, the vectors in $$V$$ are linearly independent of $$v$$. We know that there are $$p^2 + p + 1$$ linearly independent vectors in $$\mathbb{F}_p^3$$, so whenever we choose one of such vectors, we are left with a subspace of dimension 2 that does not contain the chosen vector (but contains all the others). Hence, there are also $$p^2 + p + 1$$ subspaces of dimension 2.
 * Subspaces of dimension 3: 1.

 * Subspaces of dimeansion 0: 1.
 * Subspaces of dimension 1: The number of linearly independent vectors can be calculated similarly as in a), and we get $$(p^4-1)/(p-1) = p^3 + p^2 + p + 1$$.
 * Subspaces of dimension 2: Similarly as in the case of $$\mathbb{F}_p^3$$, we have that the number of two-dimensional subspaces is $$\binom{p^3 + p^2 + p + 1}{2} / \binom{p+1}{2} = (p+1)(p^2 + p + 1) $$.
 * Subspaces of dimension 3: Similarly as in the case of $$\mathbb{F}_p^3$$, we have that for each three-dimensional subspace we have a one-dimensional subspace "left over". Therefore the number of three-dimensional subspaces is $$p^3 + p^2 + p + 1$$.
 * Subspaces of dimension 4: 1.

Exercise 5.1
Let $$V$$ be the space of symmetric and $$W$$ the space of skew-symmetric matrices. It is clear that $$\dim V = \frac{1}{2}n(n+1)$$ and $$\dim W = \frac{1}{2}n(n-1)$$ and that $$V \cap W$$ contains only the zero matrix, so the spaces are independent. By Proposition 3.6.4 b), we have $$\dim(V + W) = \dim V + \dim W = n^2 = \dim \mathbb{R}^{n \times n}$$ and so by Proposition 3.4.23, $$V + W = \mathbb{R}^{n \times n}$$.

Exercise 5.2
The condition $$\textrm{Tr}(M) = 0$$ introduces a linear dependency between the elements of the matrix. Therefore, we have $$\dim(W_1) = n^2-1$$, and thus any one-dimensional subspace of $$\mathbb{R}^{n \times n}$$ that is independent of $$W_1$$ suffices. For example we can take as $$W_2$$ the span of the matrix for which the top-left corner element is 1 and the rest are 0. Then $$W_1 + W_2 = \mathbb{R}^{n \times n}$$.

Exercise 6.1
The given vectors span the set of sequences that are constant apart from a finite set of indices.

Exercise M.3
a) Let $$x(t) = a_2t^2 + a_1t + a_0$$ and $$y(t) = b_2t^2 + b_1t + b_0$$, and $$f(x,y) = c_{2,0}x^2 + c_{0,2}y^2 + c_{1,1}xy + c_{1,0}x + c_{0,1} y + c_{0,0}$$. Then we have also $$f(x(t),y(t)) = d_4t^4 + d_3t^3 + d_2t^2 + d_1t + d_0$$. The coefficients $$d_i$$ are linear in the coefficients $$c_{j,k}$$, so

we can solve as follows

$$\begin{array}{lcl} d_4 & = & c_{2,0}a_2^2 + c_{0,2}b_2^2 + c_{1,1}a_2b_2 \\ d_3 & = & 2c_{2,0}a_2a_1 + 2c_{0,2}b_2b_1 + c_{1,1}(a_2b_1 + a_1b_2) \\ d_2 & = & c_{2,0}(a_1^2 + 2a_2a_0) + c_{0,2}(b_1^2 + 2b_2b_0) + c_{1,1}(a_1b_1+a_2b_0+a_0b_2) + c_{1,0}a_2+c_{0,1}b_2 \\ d_1 & = & c_{2,0}(a_1^2 +2a_1a_0) + c_{0,2}(b_1^2+2b_1b_0) + c_{1,1}(a_1b_0+a_0b_1) + c_{1,0}a_1 + c_{0,1}b_1 \\ d_0 & = & c_{2,0}a_0^2 + c_{0,2}b_0^2 + c_{1,1}a_0b_0 + c_{1,0}a_0 + c_{0,1}b_0 + c_{0,0} \end{array}$$

Setting each $$d_i$$ to zero yields a system of equations

$$\begin{pmatrix} a_2^2 & b_2^2 & a_2b_2 & 0 & 0 & 0 \\ 2a_2a_1 & 2b_2b_1 & a_2b_1+a_1b_2 & 0 & 0 & 0 \\ a_1^2 + 2a_2a_0 & b_1^2 + 2b_2b_0 & a_1b_1+a_2b_0+a_0b_2 & a_2 & b_2 & 0 \\ a_1^2 +2a_1a_0 & b_1^2+2b_1b_0 & a_1b_0+a_0b_1 & a_1 &b_1 & 0\\ a_0^2 & b_0^2 & a_0b_0 & a_0 & b_0 & 1 \end{pmatrix} \begin{pmatrix} c_{2,0} \\ c_{0,2} \\ c_{1,1} \\ c_{1,0} \\ c_{0,1} \\ c_{0,0} \end{pmatrix} = 0$$.

By Corollary 1.2.14 this system has a solution where at least one of the coefficients $$c_{j,k}$$ is non-zero, so there is a polynomial $$f(x,y)$$ that is not identically zero, but $$f(x(t),y(t)) = 0$$ for every $$t$$.

b) We can solve for example $$f(x,y) = x^3 + x^2 - y^2$$ using similar approach to part a).

c) Let $$x(t)$$ be a polynomial of degree $$d_x$$ and $$y(t)$$ polynomial of degree $$d_y$$, so that $$x(t) = \sum_{i = 0}^{d_x} a_it^i$$ and $$y(t) = \sum_{i = 0}^{d_y} b_it^i$$. Let $$f(x,y) = \sum_{i = 0}^{d_y}\sum_{j=0}^{d_x} c_{i,j}x^iy^j$$ be a polynomial with unknown coefficients $$c_{i,j} \in \mathbb{R}$$. In order to have this polynomial vanish at $$f(x(t),y(t))$$, we have to solve the equations that set the coefficient of $$t^i$$ to 0 for each $$i \leq d_yd_x$$ in the polynomial $$f(x(t),y(t))$$. These equations are linear in $$c_{i,j}$$, and there are $$d_xd_y+1$$ of them. On the other hand, there are $$(d_x+1)(d_y+1)$$ variables $$c_{i,j}$$, so by Corollary 1.2.14 the linear system has a non-zero solution. Note that in part a) we restricted the degree of the polynomial $$f(x,y)$$ to 2, and thus did not end up with as many equations as in this proof.


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Mario franchise strategy guide/Enemies/Buzzy Beetle

A Buzzy Beetle (メット)　is a common enemy character in several of Nintendo's Mario games. Despite their names, buzzy beetles are not actually beetles but rather Koopa Troopas with smooth black shells that cover their heads and bodies. If Mario jumps on a Buzzy Beetle, it will hide in its shell, which Mario can then kick aside to defeat other enemies or break through brick walls. Unlike Koopa Troopas, Buzzy Beetles are resistant to fireballs due to their hard shells. The only way to permanently dispose of Buzzy Beetles are to hit them with other shells, run them down while invincible, or kick them into pits. They were the precursor to the concept of nearly invulnerable enemies with certain weaknesses, popular in strafe and shoot games.

Appearances
Buzzy Beetle appears first in the underground level of World 4-2 of Super Mario Bros., and appears in several levels afterwards. After completing the game, Buzzy Beetles appear in place of Goombas when a new game is started.

The Buzzy Beetle also appears in Super Mario Bros. 3, usually in underground levels. In this game, they not only hinder Mario from ground level, but can also walk along ceilings and drop, spinning quickly forward when they land. Although resistant to fire, Buzzy Beetles can be killed by a hammer thrown from Mario's Hammer Brother suit, similar to the Koopa Troopas. Buzzy Beetles have also appeared as enemies in the Paper Mario games. The most prominent in the first Paper Mario is Chan, a student at the local dojo. In Paper Mario: The Thousand-Year Door, Spike Tops and Buzzy Beetles are shown to be kin. Spike Tops (whose Japanese name is Togemet, suggesting a cross between Buzzy Beetles and Spinys) have red shells, can crawl on any surface, and have a single spike sticking out of it. They first appeared in Super Mario World.

Relatives include Buster Beetle and Boney Beetle. Buster Beetles walk upright, moving faster than most Buzzy Beetles. In Super Mario Bros. 3 (their sole appearance), they grab and toss the blue blocks that Mario and Luigi are able to toss. This added speed and strength are compromised by their lack of protection. Any attack can defeat them (including fire), and they cannot be kicked around in their shells.

Parabeetles first appeared in Super Mario Bros. 3. Their shells were red (there are green-shelled ones in the Super Mario Bros. 3 "lost" levels) and they flew in flocks. They were content to fly in their own path and made no effort to harm Mario. Parabeetles could be destroyed via tailspin or perhaps invincibility, but it was inadvisable to do so since they could prove helpful as "stepping stones" on Mario's aerial journeys.

Bony Beetles (Hone Met in Japan) are the animated skeletons of Buzzy Beetles; being akin to what Dry Bones is to Koopa Troopas. They appear in Super Mario World and Paper Mario. Bony Beetles pace back and forth, occasionally ducking into their shells and exposing sharp spines. When jumped on (with spikes retracted), they would shatter, but quickly reform. A cape spin would defeat them outright.

They also appear in Paper Mario, Paper Mario: The Thousand-Year Door, and Super Paper Mario.


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User:Musa Vacho77

I'm Musa from Kaduna state, Nigeria. A dedicated Wikipedian. A graduate of mass communication.

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User:Markos chala

My name is markos chala

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Skaneateles Conservation Area/Invasive species/Dipsacus

<< Prohibited invasive plants at the SCA

Dipsacus spp. (teasels)
Teasels (Dipsacus species) are common in the old fields and some more wooded parts of the Skaneateles Conservation Area (SCA).
 * Wild teasel, Dipsacus fullonum (≡ D. sylvestris ≡ D. fullonum ssp. sylvestris) is the most likely teasel to be found at the SCA.
 * Cutleaf teasel, Dipsacus laciniatus is less likely to be found at the SCA, but it is present in nearby towns Elbridge and Marcellus.
 * Fuller's teasel, Dipsacus sativus was probably cultivated in the area, but not known to naturalize, so probably unlikely at the SCA.

Invasiveness ranking for Dipsacus spp. (teasels)
The 2009 New York State invasiveness ranking assessed Dipsacus laciniatus explicitly and did not assess Dipsacus fullonum at all. However, subsequent listings from individual New York PRISMS have ranked Dipsacus fullonum as highly invasive.

 * Dipsacus laciniatus (cut-leaf teasel) is listed as highly invasive with a relative maximum score of 68/90 = 75.56% and is prohibited by New York State law.
 * Dipsacus fullonum (wild teasel) is listed as highly invasive but not regulated by state law.
 * Dipsacus sativus (fuller’s teasel) was formerly cultivated in this area but not known to naturalize.

Dipsacus laciniatus and Dipsacus fullonum are similar in appearance and are known to hybridize. The primary difference is deeply-lobed leaves of D. laciniatus.

1. Ecological impact (20/30)
1.1. Unknown impact on ecosystem processes and system-wide parameters (U)

 * Dipsacus laciniatus has been known in the U.S. since the 1800s, but specific studies on its impacts to ecosystem processes and system wide parameters are not known

1.2. Significant impact in at least one layer (7/10)

 * Large stands can significantly increase the density of the herb layer, and also significantly increasing the height of the herb layer up to 3 m.

 * Teasels significantly alter the structure of rare natural plant communities.

1.3. Major alteration in community composition (10/10)

1.4. Minor impact on other species or species groups (3/10)

2. Biological characteristics and dispersal ability (16/25)
2.1. Abundant reproduction (4/4)

 * Large plants can produce over 2000 seeds.
 * Viability is high, often ≥ 80%
 * Teasel seed bank is short lived. Less than 1% of Fuller's teasel emerged after 5 years of storage in the soil

2.2. Infrequent or inefficient long-distance dispersal (1/4)

 * Most seeds fall near the parent plant.

 * Teasel seeds are not morphologically adapted for wind dispersal. Most fall within 5 ft. of plant.
 * Occasional long distance dispersal by water and wind, possibly assisted by highways that create wind corridors, may occur despite specific adaptations

2.3. High potential to be spread by human activities (3/3)

 * Readily dispersed by mowing equipment

 * Occasionally sold for cultivation and in dried flower displays (now prohibited in NY but still picked for this purpose)

 * Roadsides, fields, and waste places. It does very well along some of the major interstates and is clearly spreading and becoming more common.

 * Dispersal along roads and waterways has been important to teasel spread in North America.

2.4. Possesses one characteristic that increase competitive advantage (3/6)

 * Perennial or biennial monocarp (i.e., dies after setting seed)

2.5. Forms a dense layer above shorter vegetation and forms dense thickets (2/2)

 * Forms a very dense tall thickety layer above shorter vegetation

2.6. Can germinate/regenerate in existing vegetation in a wide range of conditions (3/3)

2.7. Other species in the genus are not invasive in New York or elsewhere (0/3)

 * Dipsacus fullonum, D. sativum, D. sylvestris not tracked as invasive here or elsewhere.
 * D. laciniatus is not as common as the common teasel (D. sylvestris)
 * Currently (2021), a number of state and federal agencies do appear to consider Dipsacus fullonum to be invasive at some level.

3. Ecological amplitude and distribution
3.1. Large dense stands present in areas with few other invasive species present (4/4):

 * Large stands can occur over 0.25 acres sometimes in areas lacking other invasives.

3.2. Known to occur in four or more natural habitats (6/6):

 * Wetland: Freshwater marshes, Peatlands, Shrub swamps
 * Upland: Grasslands/old fields, Forests/woodlands

3.3. Can establish independent of any known natural or anthropogenic disturbances (4.4):

 * Although found in disturbed areas, also reported in undisturbed areas such as limestone fens, meadows and stream corridors.

3.4. Native range includes climates similar to those in New York (3/3)

 * Native to temperate Europe and Asia.

3.5. Present as a non-native in >8 northeastern USA states and/or eastern Canadian provinces (4/4):

 * Present in KY, IN, IL, IA, MA, MD, MI, MN, MO, NJ, NY, OH, PA, VA, WI, WV, ON, QC.


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South Park: The Stick of Truth/Attack the School

Once you have made your decision, it's time to attack the school. Head around to the side of the school, where the Goths are. If you have sided with Cartman, use Butters to heal the Goth. If you have sided with Kyle, use Jimmy's ability to walk up the handicap ramp. Head through the kitchen into the cafeteria. Shoot at the light hanging from the ceiling, then shoot the fire hose to spread the electricity. Beak your way into the air duct, and use the anal probe to teleport to the top level. Break the air grate to have it fall on an enemy. Make your way back and use Cup-a-Spell to throw a fart at the torches on the barricade. Head through and defeat any enemies that remain, then head through the double doors into the main hallway. Shoot the fire sprinkler to short out the fan, then throw a fart at the torch. Head past the barricade and into the basement.

Fight your way past the Nazi zombie hall monitors, then head into the next room. Climb up the ladder and shoot the valve. Break into the air vents and drop an air vent cover on one of the Nazis. Shoot the circuit breaker and throw a fart at the flame to take out another Nazi. Climb back down and destroy the pipe. Open the gate and pull the lever to temporarily turn off the electricity. Cross the water and defeat any remaining enemies, then head up the stairs to re-enter the hallway.

Head right and enter the main lobby of the school. Destroy the chalkboard, then use the anal probe to teleport onto the balcony. Slide down the rope on the other side, then stand by the barricade to set it on fire from the flaming poop. Once it's on fire, throw a fart at it to blow it up. Defeat the rest of the enemies, then shoot the catapult and fart on the flames to let your allies in. Head through the double doors in the back where you will fight either Stan or Butters, depending on who you supported.

Butters is the more difficult of the two bosses, as he starts with a 5-hit shield which can regenerate, can inflict damage on both opponents with his abilities, and can regain nearly half of his health points and remove all debuffs when he heals himself. Use Stan's Whirlwind or Way of the Sword abilities to whittle down his shield and Armor, then use power attacks or inflict status ailments to reduce his health as much as possible.

Stan is the easier of the two bosses, as although his attacks can be devastating, he has no shield and cannot heal himself. On his first turn he will summon his dog, Sparky, to assist him. Defeating Sparky will increase his attacks, but lower his defenses. Use Kenny's charm to lower his attacks. Otherwise, continue to whittle away at his Armor and block his most powerful attacks until he is defeated.

Once you have defeated your opponent, head up the stairs and defeat more enemies. Once they have been defeated, head to the right of your two allies and open the locker on the top row. Shoot the Chinpokomon down, as this will be your only opportunity to collect it. Head into the fifth grade classroom and befriend Lemmiwinks, as this will be your only opportunity to befriend him. Then head back to the fourth grade classroom. There, you will be faced with a choice: you must fight either Cartman or Kyle.

Cartman is capable of inflicting Slow and Burning status affects very early on with his boss-specific abilities. These can be devastating, so inflict your own status affects on him. Once his health bar is half empty, or several turns have passed, he will use a flaming fart on you. Mash the button shown to counter it with your own fart and push it back at him. This will immediately bring his HP to zero.

Kyle's first move will be Entangling Vines, which will render you unable to attack, although you can still block his attacks. Afterwards, he'll simply use his normal skills during the fight. Once his health bar is half empty, or several turns have passed, he will attempt to blow you away with his leaf blower. Mash the button shown to counter it with your fart and push the air back at him. This will immediately bring his HP to zero.

Once you have defeated your opponent, you will discover that Clyde is the one who has stolen the stick.


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Skaneateles Conservation Area/Invasive species/Reynoutria

Note that even though Reynoutria japonica was first described by that name by Maarten Houttuyn in 1777, fairly recent sources have placed it and other Asian knotweeds either in Polygonum or Fallopia. However, the latest phylogenetic studies seem to show that a separate Reynoutria genus is waranted.

The synonymy for the knotweed species covered here is:
 * Japanese knotweed: Reynoutria japonica ≡ Polygonum cuspidatum ≡ Fallopia japonica
 * giant knotweed: Reynoutria sachalinensis ≡ Polygonum sachalinense ≡ Fallopia sachalinensis
 * Bohemian knotweed: Reynoutria × bohemica ≡ Polygonum × bohemicum ≡ Fallopia × bohemica

Reynoutria spp. (knotweeds)
Most Asian knotweeds (Reynoutria spp.) observed in Onondaga County have been classified as Reynoutria japonica var. japonica (Japanese knotweed), which is very common in the vicinity of the Skaneateles Conservation Area (SCA), but has not been identified within its actual boundaries (yet). It is present along Old Seneca Turnpike, a few houses to the east of the SCA, and there is a large stand along the Charlie Major Nature Trail in Mottville, a couple miles to the west of the SCA.

Reynoutria sachalinensis (Giant knotweed) is very similar to Japanese knotweed, and past observers may have confused them or their hybrid, Reynoutria × bohemica (Bohemian knotweed).

Although it only lists Tompkins County for vouchered Reynoutria × bohemica specimens, the New York Flora Atlas states that the hybrid often forms dense large monospecific stands, is widespread and often mixed with Reynoutria japonica var. japonica,

Invasiveness ranking for Reynoutria spp. (knotweeds)
The likely Reynoutria (knotweed) species in the vicinity of the Skaneateles Conservation are:
 * Reynoutria japonica var. japonica (Japanese knotweed), the most likely at the SCA;
 * Reynoutria sachalinensis (giant knotweed), less likely at or near the SCA;
 * Reynoutria × bohemica (Bohemian knotweed), which is a hybrid of previous two.

They are all considered to be very highly invasive in New York State, with a relative maximum score of 95/97 = 97.94%, and they are prohibited by New York State law. Because they hybridize extensively they were treated together for evaluating invasiveness.

1. Ecological impact (40/40)
1.1. Impact on Natural Ecosystem Processes and System-Wide Parameters (Major, possibly irreversible, alteration or disruption 10/10)

 * Slow to decompose creating an extensive organic layer (O horizon) above the soil.

 * Can limit access for fishing and wildlife, cause flooding by decreasing water flow through rivers and channels, and become a fire hazard during the dormant season.

1.2. Impact on Natural Community Structure (Major alteration 10/10)

 * Early emergence, rapid growth and persistence of dead material from previous year's growth can eradicate all layers below.

1.3. Impact on Natural Community Composition (Major alteration 10/10)

 * Forms monocultures.

1.4. Impact on other species or species groups (Severe impact 10/10)

 * Clogs waterways and lowers the quality of habitat for wildlife and fish, reducing the food supply for juvenile salmon in the spring.

2. Biological characteristics and dispersal ability (25/25)
2.1. Abundant reproduction (4/4)

 * Spread through rhizomes, root fragments, stolons, and stem fragments that can root and form new plants..

 * The extensive rhizome system can reach over 50 feet in length, allowing the plant to emerge early, shade out other vegetation, and reduce  native  species  diversity.

2.2. Numerous opportunities for long-distance dispersal (4/4)

 * Most reproduction in Japanese knotweed is believed to be vegetative, although the role of sexual reproduction is receiving increasing attention.

 * Fruits are thin and wind dispersed; plant fragments can be transported by water, with marine dispersal reported

 * Seeds do not appear to be an important means of reproduction in the United States


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Mario franchise strategy guide/Enemies/Cheep-Cheep

Cheep-Cheeps are fish-like enemies in the  franchise, first appearing in Super Mario Bros.. They are aquatic creatures that leap out of the water to attack Mario. The Cheep-Cheeps appeared in 2-3, 7-3, and a part in 8-4 (Bowser's Castle). To defeat a Cheep-Cheep on these levels, the player must simply jump on it and the player will gain 100 points. The Cheep-Cheeps were also found along with the Bloober jellyfish characters in the underwater levels 2-2 and 7-2, as well as the minus worlds and a part in 5-2. In these cases, they were immune to jumping attacks, but still vulnerable to fireballs.

One Cheep-Cheep, Sushie, was an ally to Mario in the game Paper Mario. She could shoot water out of her mouth, splash the enemies with a tidal wave, or temporarily increase Mario's defense.

Big Bertha was a giant Cheep-Cheep mother that spit out smaller Cheep-Cheeps on Levels 3-2, 3-4, and 7-4 of Super Mario 3. Its counterpart Boss Bass could leap out of water and swallow Mario whole, killing Mario instantly regardless of power-up status. Boss Bass also appears in Super Mario 64 on one level, Tiny-Huge Island, and uses the same swallowing attack.


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Mario franchise strategy guide/Bosses/King Boo

King Boo (キングテレサ) is an enemy in the Mario series of games, appearing as the boss of Luigi's Mansion and is a minor character in many Mario games. He is member of the ghost-like Boo species and looks like a larger version of the generic Boo (though not as big as Boolossus or Big Boo) with a crown on his head and a slight blueish complexion. King Boo also has a distinctive cackle that is lower in pitch than that of smaller Boos. King Boo is more of a nemesis to Luigi than to Mario.

Abilities
King Boo has shown a large array of powerful magic from the few games he's starred in, proving he is more powerful than an average Boo. These include:

Mario Party
 * The ability to steal Coins from others telepathically.

Luigi's Mansion
 * Necromancy
 * The ability to create purple fire.
 * The ability to create powerful winds (aka. Big Boo Breath).
 * The ability to become invisible (similar to other Boos).
 * The ability to go through walls (similar to other Boos).
 * Teleportation.
 * The power to create creepy and incredibly detailed mansions out of thin air.
 * It seems he can also communicate with other Boos via telepathy.

Super Mario Sunshine
 * Summon Monsters, as he summons random enemies with a slot machine.
 * Spit out regular Boos and also call them back.
 * Blow bubbles.
 * Summon coins or fruit using a slot machine.

Super Mario 64 DS
 * The ability to breathe blue fire.
 * Can manipulate mirrors, e.g. turn Mario's reflection into Luigi, go into thus mirror and attack Luigi.

Super Princess Peach
 * Can disappear and reappear any time.
 * Can shoot blue fireballs at Peach.
 * Can cry and put out the fires Peach is trying to make to destroy it

Luigi's Mansion
In Luigi's Mansion, King Boo is the leader of the evil spirits inhabiting the titular mansion and appears as the final boss, whom Luigi must defeat in order to free Mario. When Luigi reaches the mansion's secret altar, where Mario is being imprisoned in a painting, King Boo sucks Luigi into the painting of Mario, which holds a strange dimension, similar in appearance to the roof. King Boo then attacks using either Bowser's body, or a Bowser-esque robotic/magical suit, (which it is has been widely disputed among fans). Luigi must use the Poltergust 3000 ghost-catching vacuum cleaner to suck up spiked mines that the fake Bowser throws and then fire them back at it, knocking off his head and exposing King Boo to attack. King Boo has five-hundred heart points, but the health comes out of him much faster than the normal Boos.

Only in Luigi's Mansion does King Boo appear with a huge ruby for a crown, glowing pink eyes and a blue tongue. He is also roughly the same size as an average Boo. After Luigi defeats him, his crown falls off, and Luigi pries the ruby out. In later appearances, King Boo appears more like a regular Boo, with a red tongue and black eyes. However he is about 4 times the size of a normal Boo and sports a simple gold jeweled crown more like Princess Peach's. It is often thought that the Luigi's Mansion and Super Mario Sunshine versions of King Boo are different characters (implying that the name is merely a title) but this has been proven false since alot of Mario characters have changed throughout the years.

Super Mario Sunshine
King Boo is a boss of Episode 5 in the Sirena Beach level in Super Mario Sunshine. He lives below the casino of the Sirena Hotel, which, like Luigi's mansion, is plagued by poltergeists. Mario fights King Boo in a sunken room with a spinning roulette wheel as a floor and a large slot machine in its center. During the battle, Mario has to spray King Boo's lolling tongue with water to activate the slot machine, which will either send out monsters, coins, or various fruits when Boo licks it after being sprayed. If the slot machine drops a red pepper, Mario must toss it in King Boo's mouth to set it on fire, then pelt him with more fruit. In this version, King Boo appears almost intoxicated, with blue eyes (or possibly a pair of shades) and a much larger, drooling mouth with a gigantic tongue, and laughs constantly, even when he is hit.

King Boo's appearance in a casino keeps in with an association with gambling. In Luigi's Mansion, each wing of the haunted house is modelled around playing card suits.

Super Mario 64 DS
King Boo keeps his antagonistic association with Luigi in Super Mario 64 DS. In order to unlock Luigi as a playable character, the player has to enter the area called "Big Boo's Haunt" and stomp the villain by following his movements in the mirrors that line his room.

In this remake of the original Super Mario 64, King Boo appears in stages previously inhabited by Big Boo, a different, crown-less character that appeared as the boss of the Boos in Super Mario World and Super Mario 64. The character is still called "Big Boo" in-game text, but it has King Boo's trademark crown and cackle. Later appearances would feature what is clearly the same character, but under the name "King Boo." This association has led some fans to wonder if the Big Boo and King Boo are the same character or if perhaps the Big Boo is a sort of prototype for King Boo. If so, this would mean that King Boo's first appearance was in either Super Mario World or Super Mario 64, even though both games use the older name. It's also possible that "King Big Boo" is his true name, though this is unconfirmed as of yet.

Other games

 * In Mario Kart: Double Dash!!, King Boo is an unlockable heavyweight character (which is strange, because he is a floating ghost and therefore should be weightless, but his size may make up for it). His default partner is Petey Piranha. Unlike all other Double Dash!! characters, King Boo and Petey can pick up any special item from item boxes. The pair has no special item of their own. King Boo drives the Boo Pipes; although a heavy kart, it has the quick acceleration and low top speed of a light vehicle. A lack of hind limbs does not apparently prevent King Boo from reaching the accelerator pedal.
 * King Boo also appears alongside many other minor Mario characters as a teammate in Mario Superstar Baseball. He is mainly a power hitter. His bat is a staff with a crown on it.
 * The current King Boo reappears alongside other Super Mario 64 DS bosses, as a Mission Mode boss in Mario Kart DS, where Peach must face him.
 * He is the boss of World 3 of Super Princess Peach. In this game, he seems to be harmed by light, though this fact about him has never been mentioned before and is contradicted by his appearances in several other games.
 * He will have his own board in Mario Party 8.


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Super Smash Bros. series strategy guide/Characters/Master Hand

Master Hand is a fictional video game character from Nintendo's Super Smash Bros. series. It appears in both Super Smash Bros. and its sequel, Super Smash Bros. Melee. It is presumed that Master Hand will also appear in the series' forthcoming third game, Super Smash Bros. Brawl. Also, Master Hand makes several appearances in Kirby and the Amazing Mirror as a miniboss, and partnered with Crazy Hand as the boss(es) of Candy Constellation.

It is a giant white glove, similar to those that Mario himself wears. It is a right-hand glove, and it moves about by floating, with an unknown method of propulsion. General knowledge states that it is a villain, as it appears as the final boss of each game. Master Hand also has a corresponding left glove, Crazy Hand, who appears in Super Smash Bros. Melee when certain conditions are met.

The games have revealed that the Hands are a tiny link between the real world and the imaginary world in which the Smash Bros. games take place. This fits into the constant implications that the battling characters in the game are actually nothing more than toys. While Master Hand is the game's greatest opponent, it is also interesting to note that the game suggests that it gives the characters their life, a theory supported by the fact that all characters revert to their statue state when they defeat it. Whether Master Hand is merely the hand of a child with a toy collection and an overactive imagination, or a real entity with actual power is unknown.

In battle, Master Hand uses a variety of attacks, most of them related to its shape and size: it dwarfs the characters, slapping, punching, and throwing them around the platform. There are some exceptions, such as its ability to fire missiles similar to Bullet Bills and fire laser beams. Because of its size and ability to fly, it cannot be thrown off the platform as normal characters are. Instead, it has a set amount of HP which the player must bring to zero. Also, Master Hand becomes more powerful as its HP drops, as opposed to regular characters who become weaker as they accumulate damage. Master Hand's counterpart, Crazy Hand, also possesses these characteristics; however, Crazy Hand has a greater library of abilities than Master Hand (Including other strange attacks, such as dropping bombs, as well as having different effects: for instance, Master Hand's "poke" attack simply deals damage, but when Crazy Hand uses it, it freezes the target in ice on contact) and can team up with Master Hand to use still more attacks (There are three: Both hands punch together, both hands clap together, and Crazy Hand punches into Master Hand's palm. The former two begin with releasing a sleeping gas to prevent escape). Furthermore Crazy Hand is far more sporadic in combat, often prone to lengthy periods of inactivity. Crazy Hand is characterized by its twitching fingers, and is described as being the manifestation of a childish desire to destroy one's creations for amusement.

Attacks
Slap - Master Hand smashes the stage with his palm from behind. This buries the opponent upon impact.

Poke - Master Hand pokes the air, and hopefully hits his target three times.

Punch - Master Hand simply punches the ground.

Smack - Master Hand slaps the stage, but not from behind, and can be damaged while charging up.

Sweep - Master Hand moves across the stage, attacking everything along the way.

Flick - Master Hand flicks the stage, much like sweep, but the attack comes in three bursts, instead of being one big attack.

Drill - Master Hand drills the opponent into the stage. This attack is rarely fatal, but does tremendous amounts of damage.

Rocket Punch - Master Hand punches from behind the stage.

Rocket Grind - Master Hand rockets from behind the stage, and attempts to obliterate the target.

Lasers - Master Hand fires lasers from his fingertips, though only the endpoints hurt.

There are also three combination moves that are used in conjunction with Crazy Hand. They are predictable because Crazy Hand will twitch his fingers violently with small purple dots all around him right before any of the three attacks.

Double Punch - Master Hand and Crazy Hand punch together.

Fist - Crazy Hand punches into Master Hand's open palm.

Applause - Master Hand and Crazy Hand clap several times after releasing sleeping gas.

Playable Master Hand
Master Hand also can be playable, but not without an Action Replay. Also, only the controller in the GameCube's Socket 3 can control him. Crazy Hand can be playable also when plugged into controller socket 4. There have been many hoaxes created for unlocking Master Hand without an Action Replay, all of them false.


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Kirby franchise strategy guide

This Wikibook serves as a guide to video games from the Kirby franchise, including some history and trivia. This also includes recurring enemies, characters, and other subjects within the franchise.

Games

 * Mainline series games
 * Kirby's Dream Land (1992)
 * Kirby's Adventure · Kirby: Nightmare in Dream Land (1993 · 2002)
 * Kirby's Dream Land 2 (1995)
 * Kirby Super Star · Kirby Super Star Ultra (1996 · 2008)
 * Kirby's Dream Land 3 (1997)
 * Kirby 64: The Crystal Shards (2000)
 * Kirby & the Amazing Mirror (2004)
 * Kirby: Canvas Curse (2005)
 * Kirby: Squeak Squad (2006)
 * Kirby's Epic Yarn (2010)
 * Kirby Mass Attack (2011)
 * Kirby's Return to Dream Land (2011)
 * Kirby: Triple Deluxe (2014)
 * Kirby and the Rainbow Curse (2015)
 * Kirby: Planet Robobot (2016)
 * Kirby Star Allies (2018)
 * Kirby and the Forgotten Land (2022)
 * Side Games
 * Kirby Air Ride (2003)

/Enemies/

 * Poppy Bros.
 * Poppy Bros. Jr.
 * Scarfy
 * Shotzo
 * Sir Kibble
 * Sparky
 * Squeaks
 * Waddle Dee
 * Waddle Doo

/Bosses/

 * Dyna Blade
 * Fangora
 * Heavy Mole
 * Ice Dragon
 * Kabula
 * Kracko
 * Lololo and Lalala
 * Magman
 * Paint Roller
 * Whispy Woods

Final Bosses

 * King Dedede
 * Nightmare
 * Dark Matter
 * Marx
 * Zero
 * Zero Two
 * Dark Mind
 * Drawcia
 * Dark Nebula
 * Yin Yarn
 * Necrodeus
 * Magolor
 * Queen Sectonia
 * Dark Crafter
 * Star Dream
 * Void Termina
 * Fecto Elfilis

Locations

 * Fountain of Dreams
 * Green Greens
 * Pop Star

Vehicles

 * Halberd
 * Dragoon
 * Hydra

Miscellaneous

 * Magical items
 * Powers
 * Warpstar

title: Kirby franchise strategy guide


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Super Smash Bros. series strategy guide/Characters/Crazy Hand

Crazy Hand is a fictional character in the Super Smash Brothers universe. It uses attacks that generally have little to no connection with its hand shape. This is not completely true, however. Some attacks are very closely related to it (Slap), and others are somewhat related (Seizure). Crazy Hand is not usually thought of as the "main" hand, and is quite often overshadowed by Master Hand, his alter ego Crazy Hand is said to be the result of a child wanting to destroy one of his toys, while Master Hand is the result of the same child wanting to play with his toys. It is unknown whether the two of them are just the hands of a child or real beings that actually possess power. For a very brief moment in the beginning of the introduction sequence for the game, we see a Mario action figure/miniature grabbed by a hand (Without a glove and with a full arm). Whether this is one of the hands, the hand of the child playing with the toys (Meaning that Master Hand and Crazy Hand are real beings), or something completely different is unknown. When alongside Master Hand, the two of them can use combination attacks.

Crazy Hand's appearances in Super Smash Brothers Melee are as follows:
 * In single-player Classic Mode, Crazy Hand appears on Normal difficulty or higher when the player halves Master Hand's hit points in under one minute.
 * In Event 50: Final Destination Match, Crazy Hand appears alongside Master Hand with 300 hit points each. The player must take down both hands using any character to complete the event.

Attacks

 * Slap: Crazy Hand smashes the stage with his palm from behind. This buries the target in the ground on impact.
 * Poke: Crazy Hand pokes the air, and hopefully his target, three times, with the last one inducing freeze.
 * Punch: One of the simplest attacks. Crazy Hand simply punches the ground.
 * Smack: Another very simple attack. Crazy Hand slaps the stage, but not from behind and can be damaged while charging up.
 * Sweep: Crazy Hand moves across the stage, attacking everything along the way.
 * Flick: Crazy Hand flicks the stage, much like sweep, only the flicks come in bursts, instead of being one big attack.
 * Grind: Crazy Hand drills the target into the ground. This attack is rarely fatal, but does extreme amounts of damage.
 * Rocket Grind: Crazy Hand rockets from behind the stage and attempts to obliterate the target.
 * Seizure: Crazy Hand goes insane, swinging wildly to deadly effect.
 * Rocket Punch: Much like Slap and Rocket Grind, Crazy Hand punches from behind the stage.
 * Lasers: Crazy Hand fires Lasers from his fingertips, though only the endpoints hurt.
 * Bombs: Crazy Hand drops several Bombs on the field.
 * Nightcrawler: Crazy Hand forms a Spider-like pose and walks across the arena.

There are also three combination moves that are used in conjunction with Master Hand. They are predictable because Crazy Hand's fingers will twitch violently and small purple dots will appear all around him right before any of the three attacks.
 * Double Punch: Crazy Hand and Master Hand punch together.
 * Applause: Crazy Hand and Master Hand clap together many times after releasing sleeping gas.
 * Fist: Crazy Hand punches into Master Hand's open palm.

Other appearances
Crazy Hand is a miniboss (alongside Master Hand) in Kirby and the Amazing Mirror. There is also a Crazy Hand Trophy in Super Smash Brothers: Melee obtainable by clearing Adventure Mode on "Hard" or "Very Hard" difficulty with no continuations.

Trivia

 * Although Crazy Hand and Master Hand both have distinctly male voices (Heard when they enter and when they die, and are also the first tracks in the Master Hand section of the Sound Test), they are referred to as being genderless in their trophy descriptions, with the pronoun "it."
 * Many of Crazy Hand's moves have different effects than Master Hand's (Poke induces freeze, Grab induces poison, Slap induces burial, etc.).
 * The main difference between the Hand Bros. is that Master Hand is a "righty" while Crazy Hand is a "lefty".

Playable Crazy Hand
Just as Master Hand can be played with an Action Replay (Activate Debug Mode), Crazy Hand can also be played. Crazy Hand can only be played by Player 4 (A controller in Socket 4), just like Master Hand is restricted to Player 3. There have been many hoax cheats to unlock Crazy Hand without Debug Mode, all of them disproved.


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Super Smash Bros. Melee/Non-playable characters/Fighting Wire Frame

The Fighting Wire Frames are a group of enemies in Super Smash Bros. Melee. They are possibly descendants of the Fighting Polygons, or Fighting Polygon Team. It is unknown who built the Wire Frames, if anyone, but it is generally accepted that Master Hand built them, possibly with Crazy Hand's help. Their symbol is the Melee Symbol (A circle with an off-center cross), just like Master Hand, Crazy Hand, Sandbag, Giga Bowser, and the Fighting Polygons. They also have this symbol where there face should be. There are two types of Fighting Wire Frames, Male and Female. The Males have better attack and defense than the females, but the females have better speed and jumps. The Wire Frames, just like all the other NPCs, can be controlled with Debug Mode, activated with an Action Replay. The Fighting Wire Frames are very weak, with the exception of the Cruel Wire Frames found in Cruel Melee. There are a number of Multi-Man Melees, listed below:

 * 10-Man Melee: Fight 10 Wire Frames
 * 100-Man Melee: Fight 100 Wire Frames
 * 3-Minute Melee: Fight Wire Frames for 3 minutes
 * 15-Minute Melee: Fight Wire Frames for 15 minutes
 * Endless Melee: Fighting an endless number of Wire Frames
 * Cruel Melee: Similar to Endless Melee except the Wire Frames are more difficult to defeat
 * Wire Frame Fight in Adventure Mode: Fight 30 Wire Frames

The various Multi-Man Melees give different rewards, such as the unlockable character Falco for beating 15-Minute Melee and a Mr. Resetti trophy for killing 5 Cruel Wire Frames in Cruel Melee.


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Super Smash Bros./Fighting Polygons

Fighting Polygons (or "the Fighting Polygon Team") are metallic-looking purple clones of playable characters (There are no Polygons for Master Hand, Metal Mario, Giant Donkey Kong, and, obviously The Fighting Polygon Team) made completely out of polygons in Super Smash Bros.. The next to last level in the game contains 30 of these relatively weak clones of existing SSB characters.

Polygons are very weak and most can be KO'd with basic smash-attacks. The Polygons' fighting arsenal is limited to basic A-button attacks and rely moreso on their numbers than fighting skill. They retain the basic form of their character counter-parts but not weight, therefore they are easily KO'd. They stand, walk, and occasionally dash for items, however, on harder difficulty levels, the Polygons actively hunt the character down and attack in groups making them a more formidable fighting force.

Possible descendants of the Fighting Polygons are the WireFrames in Super Smash Bros. Melee, which play a similar role. They are not directly based off of any character, but the Male WireFrames are said to resemble Captain Falcon, and the Female WireFrames are said to resemble Zelda. They have approximately the same strength as the Fighting Polygons, but are somewhat more agile. It is unknown who built them, if anyone, and if anyone did build them, if the same person made both families. It is, however, a generally accepted concept that Master Hand built at least the WireFrames, as they bear its symbol. This is unconfirmed and it is not known if Master Hand built the Polygons. Crazy Hand may also have some connection.

title: Super Smash Bros./Fighting Polygons


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