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Templates:OpenRewi/Book

Templates:OpenRewi/Book-Cover

Foreword

 * Audience:tba

 * Learning objectives: tba

 * Topic: The book covers Public International Law

 * Structure: tba

This book is meant to be a living document. You will find invitations and hints for collaboration on every single page. We would be happy if you get in contact with the authors and contribute with comments. How to do that is described here.

More information about the project OpenRewi - Initiative for an Open Legal Science can be found on our website.

Suggested Citation: tba

This book is licensed under the Creative Commons BY-SA 3.0 License.

This book is also published by ... . It can be downloaded here:

In addition, this book can be purchased as a printed book: ...

Finally, the book can also be downloaded as a Word document (docx) ...

title: Templates:OpenRewi/Book


text: File:LOZthefourthbossofthefirstquest.png

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Skaneateles Conservation Area/Invasive species/Euonymus alatus

<< Regulated and other highly invasive plants at the SCA

Euonymus alatus (burning bush)
Burning bush (Euonymus alatus) is widely planted for its bright fall foliage and can easily naturalize in wooded areas, where it often becomes invasive.

Invasiveness ranking for Euonymus alatus (burning bush)
In New York State (2008) burning bush has been ranked as Very Highly Invasive with a score of 65/80 = 81.25%. and is regulated by New York State law.


text:
Template:OpenRewi/Book-Cover

 Team:

title: Template:OpenRewi/Book-Cover


text:
Template:OpenRewi/Book

Foreword

 * Audience:tba

 * Learning objectives: tba

 * Topic: The book covers …

 * Structure: tba

This book is meant to be a living document. You will find invitations and hints for collaboration on every single page. We would be happy if you get in contact with the authors and contribute with comments. How to do that is described here.

More information about the project OpenRewi - Initiative for an Open Legal Science can be found on our website.

Suggested Citation: tba

This book is licensed under the Creative Commons BY-SA 3.0 License.

This book is also published by ... . It can be downloaded here:

In addition, this book can be purchased as a printed book: ...

Finally, the book can also be downloaded as a Word document (docx) ...

title: Template:OpenRewi/Book


text: Template:OpenRewi/WIP

title: Template:OpenRewi/WIP


text: Template:OpenRewi/Advanced

title: Template:OpenRewi/Advanced


text: Template:OpenRewi/Info-top

title: Template:OpenRewi/Info-top


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Talk:Python Programming/Version history

“Recent final releases” section
Looking over the source of this page, I wonder if the latter list of “newest releases” is needed since the links above tend to always encompass them. Kdmckale (discuss • contribs) 16:49, 15 July 2021 (UTC)

After reviewing the other comments on the page and the links provided, I decided it was best to go ahead and remove the section since none of the were particularly recent, necessarily the latest of the releases for that major.minor version, or provided any additional information not contained in the major.minor link in the section above. Kdmckale (discuss • contribs) 19:46, 15 July 2021 (UTC)

“Raw source” pages
I question the links to the “raw source” pages. I’ve tested several of them and only get “data” files and nothing textual about the release. Kdmckale (discuss • contribs) 16:50, 15 July 2021 (UTC)

Necessity of Changelog links
The “What’s new” pages already contain direct links to the Changelog for each version. I don’t believe a link here in addition is necessary. Kdmckale (discuss • contribs) 16:50, 15 July 2021 (UTC)

title: Talk:Python Programming/Version history


text: Template:OpenRewi/Info-end

title: Template:OpenRewi/Info-end


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.tocnumber { display: none; }

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 * 'Back to home page'
 *  Chapter X
 *  Chapter Y: Subchapter of chapter Y

title: Template:OpenRewi/TOC


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Template:OpenRewi/Chapter

Author: Jane Doe "Required knowledge: Link" "Learning objectives: Understanding XY."

This is where the text begins. This template follows our style guide. Please take into account our guidelines for didactics. If you're wondering how to create text in Wikibooks, feel free to check out our guide on how to write in Wikibooks.

Just replace the content above and below with your content.

Further Readings

 * Source I
 * Source II

Conclusion

 * Summary I
 * Summary II

title: Template:OpenRewi/Chapter


text:
User:Alexey Vazhnov/Polish Accusative case Biernik

= Polish language: Accusative case (Biernik) =

The accusative case is used in the following situations:

 * 1) To like something:
 * 2) * lubię … —
 * 3) To eat/drink something:
 * 4) * jeść …, pić … —

 * A question for noun: Kogo? Co?
 * A question for adjective: Jaki? Jaką? Jakie?
 * Determiner: tego

For a personal names, rules are the same as for nouns.

If a noun is Rodzaj menski, but it ends like Rodzaj żeński (like tata or dentista), then the rules of Rodzaj żeński applied to this noun (but not to adjective): "mam dobr ego tat ę ".

The same as nominative case (Mianownik), for both nouns/names/adjectives in case of:
 * Rodzaj nijaki:
 * Rodzaj menski + nieżywotne:


text: Category:Book:Radio and Television

title: Category:Book:Radio and Television


text: Category:Book:Using Cakewalk by Bandlab for beginners


text:
History of video games/Platforms/Steam Deck

Development
The Steam Deck was proceeded by the Steam Machine line of console like home gaming PCs.

Development of the Steam Deck potentially dates back to September 2020.

By May 25th, 2021 reporters at Ars Technica wrote they were able to confirm some rumors that Valve was developing a portable PC codenamed "SteamPal".

The Steam Deck was announced on July 15th, 2021. The Steam Deck was announced several hours before Elgato announced a second version of their Stream Deck, causing some confusion.

The initial release date was intended for sometime in December 2021. By November 2021 logistic and supply challenges would push this date back to Feburary 2022.

Packaging for the console was revealed on December 2nd of 2021.

Launch
Steam Deck was officially released on February 25th of 2022. The console sold well at launch, with production increasing in the post launch period.

Compute
The Steam Deck appears to use a similar architecture to a PC.

The Steam Deck is powered by an AMD Van Gough APU. This APU includes a quad core Zen 2 CPU capable of executing 8 threads. The APU also includes an RDNA2 based GPU sporting 8 GPU compute units with 512 total stream processors. The system is capable of a performance of around 2 teraflops. The system supports ray tracing.

The system has 16 gigabytes of LPDDR5 RAM.

Software

Steam OS is used as the default operating system, though custom operating systems may also be installed.

Games
Unusually for a handheld gaming device, but standard for a PC Valve had no plans for exclusive titles for the Steam Deck.

Aperture Desk Job
Short tech demo game by Valve announced close to launch to demonstrate Steam Deck system features, while also being available for Steam on some other platforms.

External resources

 * Steam Deck website


text:
Traditional Abacus and Bead Arithmetic/Division/Guide to traditional division (帰除法)

Introduction
Traditional division method (TD), kijohou, guī chúfǎ (帰除法), is one of the two main methods of division used with the abacus. This method makes use of both the multiplication table and a specific division table and has been the standard method studied with the abacus for at least 4 centuries, losing popularity in the 1930s. As a digit-by-digit or slow division algorithm, has been introduced in the previous chapter, where its special characteristic is revealed: it does not require thinking but only following some rules. This document is an introduction to its use on the abacus and it is assumed that the reader is already proficient in the modern division (MD) method.

The division table
In the previous chapter ../Modern and traditional division; close relatives/, the following division table has been introduced

where in each cell the result of the Euclidean division $$(10\times a)/b=q,r$$ ($$q$$: quotient, $$r$$: remainder, $$a,b$$ digits from 1 to 9) is expressed in the form $$a/b>q+r$$ for reasons that we will see below. This means that the following hold:

$$10a=q\cdot b+r$$

The table has three zones corresponding to the following: If the divisor has $n$ figures and we compare it with the first n digits (from the left) of the dividend, with added trailing  zeros if necessary, three cases can occur:

 * 1) the dividend is greater than or equal to the divisor (ex. $$770/689$$)
 * 2) the dividend is less than the divisor and the first digit of the divisor is equal to the first digit of the dividend (ex. $$670/689$$)
 * 3) the dividend is less than the divisor and the first digit of the divisor is greater than the first digit of the dividend (ex. $$570/689$$)

The blank cells below the diagonal of the division table above correspond to case 1. They could be filled in the style of the tables that can be seen elsewhere, but we leave them empty for simplicity. If during the division we fall into this zone, we will proceed, for now, simply by revising up the previous quotient digit as we will see in the examples that follow.

The diagonal elements (in gray) correspond to the case 2 and can only occur if the divisor has at least two digits.

Finally, the other non-diagonal elements correspond to the case 3, which can be considered the most important to study.

There is no doubt that memorizing the division table takes time and effort and that you want to know if the traditional method of division is right for you before investing so much time and effort. Fortunately, the division by nine, five, and two tables are remarkably simple and can be memorized almost instantly (see below), as well as diagonal elements for multi digit divisors. This means that we can learn this traditional technique using divisors that start with only 9, 5 or 2 without much effort and thus be able to decide whether it is worth spending time learning the whole table or not. In what follows we will use examples based on such divisors.

Why do the division rules include remainders?
Suppose we are going to divide 35 by 9, the 3/9>3+3 rule tells us that we must use 3 as an interim quotient and the next step will be to subtract the chunk 3✕9=27 from 35, leaving a remainder of 8. If we also memorize the remainders, we can save this multiplication step as follows: we cancel, clear or erase the first digit of the dividend, in this case 3, then we add the remainder (3) to the next figure (5) of the dividend. In this way, we obtain the same result but without using the multiplication table. With one-digit divisors we will never have to resort to the multiplication table, and in the case of divisors with several figures, proceeding in the same way, we will save one of the necessary multiplications. We will see it on the abacus below, but first we need a few words about how we are going to arrange the division on the abacus.

Modern Division Arrangement (MDA)
It is am assumed throughout this textbook that the reader has already studied the modern abacus method, as typified in the work of Takashi Kojima. In the following examples we will illustrate traditional division using the same division layout that you are already familiar with so that you can more easily follow them and use your usual 4+1 type abacus if you want. We will call this layout Modern Division Arrangement (MDA), but this is not the way division was traditionally organized on the abacus. Later, I will introduce the Traditional Division Arrangement (TDA) which, as we will see, it has some advantages and some disadvantages, including the need (or at least the convenience) of using a specialized abacus with additional upper beads.

While using MDA you can use the same rules you already know about the unit rod if you need them.

Let us see the 35÷9 case  from the above section, first without using the (rule) remainders

And now using the remainders

That is:

One digit divisors
The number 123456789 has traditionally been used to demonstrate the use of multiplication and division tables in ancient Chinese and Japanese works. Here we will use it with the “easy divisors” 9, 5 and 2.

Multi Digit divisors
Consider, for example, $$359936/9728=37$$, in this case it is convenient to think of the divisor as made up of a divider, the first digit, followed by a multiplier, the rest of the digits of the divisor, that is, $$9728 = dmmm$$, where $$d$$ is the divider (9) and $$mmm$$ is the multiplier (728). The Chinese and Japanese names for this division method (帰除 Guīchú in Chinese, 帰除法 Kijohou in Japanese) refer to this: 帰, Guī, Ki is the header and 除, chú, jo is the multiplier.

In this case, the way to act is as follows:

 * 1) First we consider only the divider $$d$$ and do exactly the same as in the case of the single digit divisor i.e. we follow the division rule: get the interim quotient $$q$$ and add the remainder (from the rule) to the adjacent column
 * 2) Then we subtract the chunk $$q\times \text{multiplier}$$ from the remainder if we can; otherwise we have to revise down $$q$$ and restore $$d$$ to the remainder using the following rules:

These rules are for two-digit divisors, for divisors with more digits things may be more complicated, as in MD (see example $$23712/5928$$ below). Let us see the above case

Example 359936÷9728=37
Note: This is an abbreviated notation meaning that 3✕7, 3✕2 and 3✕8 have to be subtracted from IJ, JK, and KL respectively.

Traditional Division Arrangement (TDA)
As commented above, there are two basic ways of arranging general division problems. Let us see them side by side:

 * Modern division arrangement (MDA), as explained by Kojima ,

 * Traditional division arrangement (TDA), as used in ancient books since the times of counting rods to the first part of the 20th century ,

So far we have used MDA with the traditional division without any problem. TDA, however, is problematic with any division method, the traditional one included. This troublesome nature is due to a collision between the divisor and the dividend/remainder that occurs frequently (that is, both require the simultaneous use of the same column), and special techniques or abaci are needed to deal with this collision. Despite this, the TDA has been used for centuries in conjunction with the traditional method of division, at least since the 13th century, while the MDA has been shelved until modern times. It is clear that certain advantages can be recognized to TDA, but it is not so clear that they are enough to justify its historical use:

 * It uses one rod less
 * Result does not displace too much to the left as in MDA, which is of interest in the case of chained operations. This and the above points makes TDA more suitable to abacuses with a small number of rods, like the traditional 13-rod suanpan/soroban.
 * It saves some finger movements; for instance, in the operation 6231÷93=67 using traditional (chinese) division, I count 14 finger movements with TDA versus 24 with MDA.
 * Hand displacements are shorter.
 * It is less prone to errors as less rods are skipped.

The way to avoid the mentioned collision is to accept that the first column of the dividend/remainder, after the application of Chinese division rules, can overflow and temporarily accept a value greater than 9 (up to 18), while providing some mechanism to deal with such an overflow. Interestingly enough, it seems that no ancient text explains how to do the latter, but we will do it in chapter: Dealing with overflow!.

In the case of a 5+2 or 5+3 abacus we can use the additional upper bead(s) to represent values from 10 to 20, using the suspended bead (懸珠 xuán zhū in Chinese, kenshu in Japanese) in the 5+2 case.

The third or suspended bead is expected to be used only in about 1% of cases, which justifies the adoption of the 5+2 model as standard instead of the 5+3. (If you are interested in using TDA on any abacus, head over to the Dealing with overflow chapter to see how)

For examples of TD using TDA, refer to the Traditional division examples chapter.

About the efficiency of TD
As you can see in the examples with single digit divisors, TD efficiency deteriorates as the divisor starts with lower figures in the sense that we have to revise up more frequently. We can say that the efficiency is zero when the divisor starts with 1; in fact, we don't even have division rules except 1/1>9+1 (which is statistically excessive, see chapter: Learning the division table). For this last case, the trick is to divide by 2 in situ (chapter: Division by powers of two) both divisor and dividend, which is very fast, and proceed to divide both results normally; now the divisor begins with a digit between 5 and 9. for example: $$128/16$$

$$128/16 = (128/2)/(16/2) = 64/8 = 8$$

In other cases, our intuition and experience with MD could help us.

This lower efficiency of TD compared to MD is the price to pay to save us the mental work of deducting the interim quotient figure that we have to try.

Further readings

 * deals with traditional division


text:
Oliver Twist/Plot Summary

'Oliver Twist' The Parish Boy's Progress is a book in which Oliver Twist is a nine-year-old orphan boy who doesn't know who his parents were. He escapes from a workhouse to London where he meets the 'Artful Dodger'(Jack Dawkins), who is leader of the gang of the juvenile pickpockets. Fagin, the leader of a criminal gang of boys, he trains Oliver for unlawful activities, which was unfamiliar to Oliver. And this is how Oliver started passing his life with criminals. At the end of the story he has escaped and is living with his Aunt Rose, and "Great-Uncle" Edward Brownlow and all the criminals were caught and were imprisoned.

title: Oliver Twist/Plot Summary


text:
Oliver Twist/Story

Story
In Victorian times, a young woman named Agnes Leeford is pregnant and walks all the way to a workhouse in an unnamed city in England. She enters the workhouse and then has her baby - a boy. She dies before she can name him. Sally, an old woman who worked at the workhouse, takes care of the baby. Mr Bumble, the head of the workhouse, surnames the new workhouse children by alphabetical order. He comes to 'T' and names him Oliver Twist.

Nine years later, Oliver is a workhouse-boy. In his room, the boys have a dare and Oliver got the shortest straw. Because of this, he has to ask the dining hall master for more Gruel. This angers The Parish Board and they sell Oliver for £5, wanting to get rid of him. A man named Mr Sowerberry buys him. When Oliver is at his house, a teenager named Noah Claypole bullies Oliver about his mother. Oliver punches Noah, but only gets himself into trouble with Mr Bumble, who Noah tells to come round. Oliver is let out of the cellar and is whipped by Mr Sowerberry. He escapes and walks for seven days to London. When he is there, a boy named Jack Dawkins (who is better known as the "Artful Dodger") takes Oliver to the loft where he lives with other boys. Oliver meets Fagin; an old man; Nancy, a woman who grows to care a lot about Oliver, and Bill Sikes, Nancy's boyfriend who is a murderer. Fagin, Dodger, and a boy named Charley Bates teach Oliver how to steal. Oliver doesn't realise they are thieves. The next day Oliver, Dodger and Charley go out to steal. Dodger and Charley steal a handkerchief from an old man called Mr Brownlow. Oliver is frightened and runs off, which causes Mr. Brownlow to think he’s the thief. After a chase where Oliver is hurt, he is taken to court, faints and is almost carried off as guilty, but the bookkeeper tells everyone he saw the real thieves (Dodger and Charley). Mr. Brownlow rushes him to his house and cares for him while he recovers from a fever.

Oliver faints and the next thing he knows, he is on a bed. He sees two women. Rose (his Aunt) and Mrs Bedwin (the housekeeper). He is cared for better than he ever has been, and everyone likes and trusts him. Meanwhile, Fagin and Bill get really angry with Dodger. Bill tells Nancy to look for Oliver and bring him back. Oliver is told to go to return some books to the bookkeeper, but Nancy catches him. Oliver screams saying he doesn't know them, but nobody believes him. When he returns, the other boys bully him for his fancy clothes. Meanwhile, Edward Brownlow (known as Monks), Oliver's half-brother, wants Oliver dead. They had the same father. Monks secretly tells Fagin if he wants a few coins, he'll have to murder Oliver, and if not then Monks will do it himself. Nancy hears all this so she tells Mr Brownlow at the old bridge at midnight. Dodger hears this, and tells Fagin that Nancy has betrayed everyone. Sykes secretly hears and murders Nancy. He takes Oliver for a long walk with his dog Bullseye. When Bill is trying to escape, he accidentally hangs himself. Oliver is reunited with Mr Brownlow and Rose. Monks is ultimately arrested.

title: Oliver Twist/Story


text:
User:Admazzeo/sandbox

Projects

 * TestSubpage

title: User:Admazzeo/sandbox


text:
User talk:WikiMathematician

Welcome, Kdmckale!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. JackPotte (discuss • contribs) 13:09, 16 July 2021 (UTC)

title: User talk:WikiMathematician


text:
Mechanics of Materials

Author(s): Aaron D. Mazzeo

Chapters and Syllabus for Printable PDF

 * /Background/
 * 1. Introduction to Mechanics of Materials
 * 2. Physical Units and Standards
 * 3. Static Equilibrium
 * 3.1 Free Body Diagrams
 * 3.2 Static Form of Newton's Second Law of Motion
 * 3.3 Static Equilibrium of Trusses
 * 3.4 Static Equilibrium of Beams

 * 4. Axial Loading
 * 4.1 Bars as Springs
 * 4.2 Axially Loaded Bars in Series and Parallel
 * 4.3 Indeterminate Axial Loading of Bars

 * 5. Stress and Strain
 * 5.1 Normal Stress
 * 5.2 Shear Stress
 * 5.3 Normal Strain
 * 5.4 Shear Strain
 * 5.5 Stress and Strain in a Bar

 * 6. Material Properties
 * 6.1 Stress-Strain Relationships for Ductile Materials
 * 6.2 Stress-Strain Relationships for Brittle Materials
 * 6.3 Poisson's Ratio
 * 6.4 Modulus of Resilience
 * 6.5 Fatigue
 * 6.5 Uniaxial Failure from Yielding
 * 6.6 Material Selection Charts

 * 7. Material Testing
 * 7.1 Tensile and Compressive Tests
 * 7.2 Fatigue Testing

 * 8. Torsion
 * 8.1 Angular Displacement in a Twisted Rod
 * 8.2 Shear Strain in a Twisted Rod
 * 8.3 Elasticity of a Twisted Rod

 * 9. Beam Bending
 * 9.1 Relationship between Moment and Curvature
 * 9.2 Displacement across a Beam
 * 9.3 Statically Indeterminate Beams
 * 9.4 Typical Beam Bending Conditions, Displacements, and Slopes

 * 10. Combined Loading
 * 10.1 Stress Transformations
 * 10.2 Mohr's Circle for Stress
 * 10.3 Shear Transformations
 * 10.4 Mohr's Circle for Strain

 * 11. Failure Criteria for Static Loading
 * 11.1 Maximum Normal Stress
 * 11.2 Maximum Shear Stress
 * 11.3 Maximum Distortion Energy
 * 11.4 Safety Factors

 * 12. Pressure Vessels

 * 13. Beam Buckling

title: Mechanics of Materials


text:
User talk:Sruiperez

Wrong language?
This is the English Wikibooks. Are you looking for the Spanish Wikibooks? Leaderboard (discuss • contribs) 19:07, 16 July 2021 (UTC)

title: User talk:Sruiperez


text:
International Postage Meter Stamp Catalog/Eswatini (Swaziland)

=Eswatini (Swaziland)=

 * The first meter appeared in the early 1960s when the country was a British protectorate.
 * Meter stamps issued during the protectorate period are inscribed “SWAZILAND”. In 1968 the country achieved independence, and meter inscriptions were changed to “KINGDOM OF SWAZILAND”. In 2018 the contry's name was changed again to the Kingdom of Eswatini.

 * The stamps are grouped according to period of issue and inscription:
 * A - Issued under period of British protectorate, inscribed “SWAZILAND”
 * B - Issued since independence, inscribed “KINGDOM OF SWAZILAND”

 * C - Issued since name change to Kingdom of Eswatini (no stamps reported as of 2021)

GROUP A: First issued during period of British protectorate, inscribed “SWAZILAND” alone

'''A1. Neopost “105” ''' (LV-6). [$25]
 * Upright frank with straight single-line border.
 * Crown and “EiiR” in center below country name.
 * M# with “NB” prefix, NB528 seen.
 * TM: BIC
 * Values seen: MeterCat 5 spaces.jpg 2½, 3c

'''A2. Universal “Simplex” ''' (LV-21). [$5]
 * Upright frank with simulated perforation outer border and straight-line inner border.
 * Large crown at bottom center below value figure.
 * M# with “S” prefix in boxes in lower corners.
 * TM: DC
 * £sd values seen: MeterCat 5 spaces.jpg 3, 4½, 7, 9D, =1/-
 * Decimal values seen: MeterCat 5 spaces.jpg 2½, 3, 3½, 5, 6, 7, 12½c

'''A3. Universal “Simplex” ''' (LV-21). [$10]
 * As Type A2 but without crown, blank at bottom center.
 * M# with “S” prefix.
 * TM: DC
 * Decimal values seen: MeterCat 5 spaces.jpg 2½, 3, 3½c

'''A4. Pitney Bowes-GB “Simplex” ''' (LV-21). [$5]
 * Small, square frank with large value figure in center.
 * M# with “S” prefix in boxes in lower corners.
 * A. Value figure wide, serifed (as pictured)
 * B. Value figure smaller, san-serif (not shown)
 * TM: DC
 * Values seen: MeterCat 5 spaces.jpg 2, 3, 4, 5, 6, 10c

'''A5. Universal “Automax” ''' (MV). [$5]
 * Similar to Type A4 but larger frank with narrower spacing.
 * M# with “UA” prefix.
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg .00=

'''A6. Universal “Automax” ''' (MV). [$5]
 * Upright frank with single line simulated perforation frame and no inner panels.
 * "POSTAGE" reads up at left, "REVENUE" reads down at right.
 * Meter number at lower right with "UA" prefix at lower left.
 * M# “UA 1” only seen.
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg .00=

'''A7. Pitney Bowes “5000” ''' (MV). [$5]
 * Square frank with meter number in boxes below country name at top.
 * Value figures below level of date figures.
 * M# with “PBH” prefix.
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg 0 .00(½)

'''A8. Neopost "Frankmaster" / "305" ''' (MV). [$5]
 * Frank similar to Type A6 but with panels at top and bottom and blank at sides.
 * Country name in top panel, “POSTAGE PAID” in bottom panel.
 * M# with “R” prefix (R 293 seen).
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg 0•00=

'''A9. Neopost “205” ''' (MV). [$5]
 * Upright frank with single straight-line border.
 * Country name in panel at top.
 * M# with “J” prefix at bottom (J 279 seen).
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg 0•00 –

'''A10. Hasler “Mailmaster” ''' (MV).
 * Large square frank with double straight-line outer border and country name repeated in panels at top and bottom.
 * “POSTAGE PAID” vertical at both sides.
 * M# with “HAS” prefix above bottom panel.
 * TM: DC
 * V/F: MeterCat 5 spaces.jpg 00.00

GROUP B: Issues since independence in 1968, inscribed “KINGDOM OF SWAZILAND”

 * Note that stamps unaltered from the British protectorate period continued to be used well after 1968.

'''B1. Pitney Bowes-GB “Simplex” ''' (LV). [$20]
 * Similar to Type A4 but with revised country name and with line ornaments in the corners.
 * M# breaks bottom frame line.
 * One meter number seen, “P.B./S/3-75”.
 * TM: DC
 * Value seen: 5

'''B2. Pitney Bowes “6300” ''' (MV).
 * Very similar to Type B1 but narrower spacing.
 * The corner ornaments vary in length from one meter to another.
 * M# breaks bottom frame line.
 * A. M# with “PBL” prefix
 * B. M# with “P.B.” prefix
 * C. M# with “SG” prefix
 * D. M# with “P.B./S/1-“ prefix (P.B./S/1-74 seen)
 * TM: DC
 * V/F: 0.00(½)  00.00 MeterCat 5 spaces.jpg 0.000

'''B3. Neopost “105” ''' (LV). [$5]
 * Upright frank with straight single-line border and value figure boxed in center.
 * “KINGDOM” in panel at top, “OF / SWAZILAND” below center box.
 * “POSTAGE” and “PAID” reading up at the sides.
 * M# with “NB” prefix flanking “OF”.
 * M#s 1469 and 1470 seen.
 * TM: DC
 * Values seen: 2, 3, 5, 10c

'''B4. Neopost “205” ''' (MV). [$5]
 * Similar to Type B3 but value inside inner panel that extends to right side, and “POSTAGE / PAID” reading downward at left.
 * M# with “J” prefix, J92 seen.
 * TM: DC with tall date figures
 * V/F:  00 –

'''B5. Neopost “205” ''' (MV).
 * As Types B3 and B4 but without inner box.
 * “KINGDOM OF” breaks top frame line. Inner frame line below “SWAZILAND” broken by small “POSTAGE PAID”.
 * Very small M# “H 169” at bottom.
 * A. M# “H 169” very small at bottom
 * B. Mailer’s name between and below M#. M# “RS 157” (USUTU/ PULP CO. LTD.) MeterCat 5 spaces.jpg[$10]
 * TM: DC
 * V/F:  0,00  0;00

'''B6. Neopost “2205” ''' (MV).
 * Similar to Type B5 but wider frank.
 * Country name does not break top frame line.
 * “POSTAGE PAID” reads up at left.
 * A. M# “2 X 1323W”
 * B. Mailer’s name below M#. M# “2 X 1419W” (USUTU PULP CO. LTD)
 * TM: BIC with short date figures
 * V/F:  0,00

'''B7. Neopost “2205” ''' (MV). [$15]
 * Frank tall and narrow.
 * Country name at both top and bottom.
 * “POSTAGE / PAID” reads up at left.
 * M# with “RS” prefix below country name at top.
 * One seen: RS 697
 * TM: BIC
 * V/F:  0,00

'''B8. Neopost “Electronic” ''' (MV).
 * Large frank with single straight-line border.
 * Country name at top, M# at bottom center.
 * A. “POSTAGE PAID” vertical at both sides. M# without prefix (2442 seen)
 * B. “POSTAGE PAID” at left only. M#s "G355017", “G66262” and “GN929N” seen
 * TM: DC
 * V/F: ≋0,00

'''B9. Neopost “Electronic” ''' (MV).
 * Frank with simulated perforation border with enlarged corners.
 * “KINGDOM OF” at top and “SWAZILAND” at bottom.
 * M# with “ET” prefix in lower corners.
 * M#s 4056 and 4758 seen.
 * A. Frank 25½ mm tall (4056, 4751)
 * B. Frank 27 mm tall (4758)
 * TM: DC
 * V/F: ≋0,00

'''B10. Neopost “Electronic” ''' (MV).
 * Horizontal frank with straight-line border, value figures boxed in center, and panel containing “KINGDOM OF” at top.
 * M# with “ET” prefix.
 * TM: DC
 * V/F: ≋0,00

'''B11. Francotyp-Postalia “EFS3000” ''' (MV).
 * Large frank with simulated perforation border.
 * “POSTAGE PAID” at top and repeated upside down at bottom.
 * Country name reads down at left.
 * M# also reading down inside country name.
 * M# 591306 seen.
 * TM: SC
 * V/F:  00.00

NOTE: See the NOTE below Type B12.

'''B12. Francotyp-Postalia “EFS3000” ''' (MV).
 * As Type B11 but the country inscription and meter number are at right rather than at left.
 * TM: SC
 * V/F: 00.00

NOTE: Both the B11 and B12 stamp dies appear to have been mounted incorrectly in their respective machines so that the country name appears at the sides rather than at the bottom where it was most likely intended to be. Stamps from Francotyp-Postalia "EFS3000" machines probably exist with country inscription at bottom, but they have not been seen by or reported to us.

---


text:
Mario & Luigi: Partners in Time/Plot Summary

Shroob invasion of Mushroom Kingdom
The Shroob invasion of Mushroom Kingdom was an invasion that was the key focus of the 2005 game Mario and Luigi: Partners in Time. For centuries, a species of mushroom-like aliens called the Shroobs inhabited a planet in a faraway galaxy called Shroob Planet. Their planet, which looks exactly like a huge giant mushroom in the middle of space, was deteriorating in life quality so these aliens stared into space to find a new home. Finally, one day, they stumbled upon a beautiful place here on Earth known as the Mushroom Kingdom and the Shroobs knew there was no turning back now.

Invasion
When Mario and Luigi were babies, they were at Peach’s Castle with Toadsworth and baby princess Peach. Mario and Luigi walked into the throne room to play with Peach, but right when the play date was about to start, Baby Bowser suddenly dropped to the floor from a high altitude and breathed fire on Toadsworth, knocking him out. After fainting for about ten seconds, Toadsworth regained consciousness and taught baby Mario how to attack by jumping. Mario managed to knock out Bowser after a gruesome battle lasting four minutes. During those four minutes, Luigi still got to enjoy some quality time with Peach. As if Bowser’s intrusive visit wasn’t traumatizing enough, the residents of Peach’s Castle had no idea that it was going to get a heck of a lot worse. Being assaulted by Bowser that morning was nothing compared to the ordeal that lay ahead of them. Moments later, the Shroob invasion began. These aliens began firing lasers and missiles into the castle. A Shroob spaceship became fully charged for their attack and if this attack hit, it would nuke the entire room, killing everyone inside. Toadsworth told everyone to flee as he declared that the castle is lost.

Luckily, Baby Bowser launched a spike ball from his Koopa Cruiser, hitting the spaceship spot on, and rescuing baby Mario, baby Luigi, baby Peach, and Toadsworth. They grieved as reality smacked them hard: Their once beautiful castle was lost. As they faced their brutal new reality, they knew they had a long, painful road ahead of them. Meanwhile, adult Mario and adult Luigi traveled to Hollijolli Village and rescued the mayor of the village. Seconds later, the mayor was knocked out and abducted by three Shroobs. Mario and Luigi then fight the Shroobs, but despite the brothers’ best efforts, they were obliterated by the Shroobs. One of them was holding a remote control for a bomb UFO that would detonate after three turns. Upon detonation, the UFO released so much explosive energy that Mario and Luigi were instantly knocked unconscious. The Shroobs celebrated their victory by repeatedly laughing at the fainted Mario and Luigi, laughing and jumping up and down repeatedly for minutes on end. Meanwhile, baby Mario and baby Luigi had been in Bowser’s Koopa Cruiser, flying high up over the village. Baby Bowser fires a spike ball from the cannon on the Koopa Cruiser, firing in the direction of the three Shroobs, killing one and knocking the other two flying, buying them time to lower the Koopa Cruiser down into the village and send the babies to rescue Mario and Luigi. With the help of Toadsworth, who was generous and gave the babies a lifetime supply of Green Shells, the babies defeated the two remaining Shroobs and rescued Mario and Luigi. After they are reunited on the Koopa Cruiser, Toadsworth explains the events of that morning, and how they were rescued by Baby Bowser.

After the heartless attack, the castle was badly transformed, with purple mushrooms growing on the exterior and interior of the castle, and the floors, walls, and ceilings became a variety of shades of purple, the same color as the Shroob intruders. As the cruiser flies past the now uninhabitable castle, Mario talks to Toadsworth, who was taken aback to learn that the adults were the future versions of Mario and Luigi who had traveled back in time in hopes of rescuing princess Peach. A minute later, the Koopa Cruiser’s alarm goes off a second time as it correctly detects another Shroob missile. Unfortunately, the Koopa Cruiser failed to avoid the attack; the direct hit sent the cruiser crashing straight into Bowser’s Castle. Toad Town was also badly deformed by the invasions.

Back to the present
After Mario and Luigi work their way to the time hole at the end of Bowser’s Castle, they, along with the babies, go back to the present Peach’s Castle and inform Professor E Gadd of their discoveries. They found a piece of the Cobalt Star, which causes the Junior Shrooboid to go nuts, and opens a time hole to Toadwood Forest. Inside the forest, the quartet is horrified to discover trees where Toads had been enslaved and bound to the trees. The Toads’ energy was sapped by the trees and the energy was converted to a Shroob drink called “vim” at the Vim Factory. The four brothers burned down a forest that was blocking the entrance to the factory and took a pipe to enter the factory. Their friends, the Hammer Bros, had been brainwashed by the Shroobs, and threatened them in the Leet (1337) Internet language. The babies were unharmed but were forced to fend for themselves as Mario and Luigi were carried away by a suction tube to a tree elsewhere in the factory. After the babies defeat the Hammer Bros, the Hammer Bros faint, losing the antennae that caused them to obey the Shroobs; thus, the Hammer Bros reverted to their usual selves, and taught the babies how to use hammers to destroy crates that would otherwise block the path. The babies walked into the vents of the factory where they were ambushed by two Spiny Shroopas and learned from the Hammer Bros how to fight with hammers, as the Spiny Shroopa is a spiked species that cannot be attacked by jumping. The babies defeat the Shroopas, fall out of the vents and destroy the tree where Mario and Luigi were immobilized and enslaved, freeing them, but not without another Spiny Shroopa ambush.

The Hammer Bros teach all four brothers how to fight with hammers as a full team of four. Then, the babies explore the rest of the factory until they encounter Swiggler. After defeating Swiggler, the brothers collect the second Cobalt Star fragment, but Baby Bowser intervenes and steals both Cobalt Star fragments and Kamek helps him retreat to Yoshi’s Island. Mario, Luigi, baby Mario, and baby Luigi go to Yoshi’s Island to track down Bowser and Kamek. The quartet is victorious, but unfortunately their victory is overshadowed moments later as a Shroobified Yoshi-like creature called the Yoob, swallows the quartet as prey. The quartet is moderately injured from the fall from the Yoob’s throat to the stomach floor but eventually leaves the Yoob’s stomach unharmed. They manage to get the Cobalt Star shards back. Then, Mario and Luigi and the babies go to Gritzy Desert, and then to Thwomp Volcano, where they witnessed the annual eruption of the volcano. The volcano erupts for days on end, making Mr. Thwomp and Mrs. Thwomp very elated and happy. Mario and Luigi and the babies try to take shelter in a laboratory run by Professor E Gadd, but are unable to escape the flames. The babies managed to extinguish the flames on the burning Thwomps in the laboratory, but more kept falling. The eruption ended at last, but not before extensive damage occurred. The laboratory was completely destroyed, forcing Professor E Gadd to start from scratch in a new laboratory at Boo Woods.

The quartet goes into the volcano’s caverns to rescue who appeared to be Peach, but the quartet was abducted by a Shroob alien ship that takes them to Toad Town. The Peach lookalike takes off her disguise and reveals herself to be Princess Shroob herself. After making their way through Toad Town, the quartet climbs the Star Hill, visits the Star Shrine, and collects the fifth Cobalt Star fragment. With that, they gain access to Shroob Castle and discover that the castle has been largely transformed, though the structure of the rooms is still largely recognizable. The hallway and throne room where the babies once played with Peach were completely blocked off by a laser beam system. The quartet roams the first floor to get all laser beams to point to the Shroob ship in the room that was once the hallway where baby Mario and baby Luigi began their journey. They still cannot enter the throne room, where a locked gate denies their entry. They instead take the underground sewers to get to that room. Eventually, they rescue Peach and stop the Shroob invasion.


text:
South Park: The Stick of Truth/Beat Up Clyde

Use Butters to heal Wendy, then use Nagasaki to destroy the two gargoyles along the drawbridge. After advancing across the moat, you will have to options for entering the fortress. The first is to teleport up to the generator, disable it, then defeat the guards and enter through the front gate. The second is to head to the back of the base, shrink yourself down with the Gnome Dust, and enter the hole. Use Butters to heal the gnome, who will proceed to kill one of the Nazi Zombie Rats. Shoot the lighter and fart on the flames to take out the second rat. Continue on and shoot the floorboards to create a ramp into the fortress.

If you entered through the main gate, use Kenny to trick the guards into destroying the barricade, then head past them and shoot the ladder down (if you entered through the gnome hole, you will have to defeat the guards on your own). Climb up the ladder and defeat the guards, then climb up the next ladder and defeat the Nazi zombies. Once they are defeated, break the platform's leg and use Nagasaki to create a ramp. Climb up it, then climb up the ladder to the roof of the fortress.

There are two towers, one on the left and one on the right. Fart on the firework to send it into the tower on the right, then use Nagasaki to finish it off. Turn the wheel to partially raise the gate. Teleport to the highest level to collect an exclusive Chinpokomon, then shoot the lantern and fart on the flames to destroy the second tower. Turn the wheel on the left to completely raise the gate, then head inside.

Inside you will find Craig, who is beginning to raise a third Nazi Zombie Cow. Shoot the lantern on the left and fart on it to let Stan in, then use Nagasaki to break a hole in the right wall and let Ike in. When both cows are defeated, Craig will jump down with his remaining cow and attack.

If you have failed to kill the other two cows in time, you will have to fight them alongside Craig. Don't bother attacking them, as they will explode when they attack. Target Craig with your strongest attacks, especially ones that lower armor. At a certain point, Craig will create multiple clones of himself. Use a ranged weapon that will hit multiple enemies, such as Chakram or a Super Bouncy Ball. One of the clones will either be African-American or Asian, making the imposter obvious. Craig will summon more clones if the first batch is defeated, so leave one clone alive if possible. When Craig is defeated, climb up the ladder and head into the next room.

Enter the next room, then shrink down and enter Mr. Slave's butt. Make your way forward, destroying the semen walls in your way. Eventually you will be attacked by a group of bacteria, so fight them off. Climb up the ear of corn, then use Stan's buddy ability to turn off the electrical current. Afterwards, shoot the red puss-sack, then use your anal probe to teleport over. Defeat the bacteria and keep moving forward.

Climb up Mr. Hat, then destroy the billiard ball with Nagasaki. Keep moving forward and answer the phone to become friends with Big Gay Al. Fight off more bacteria, then keep moving. Climb to the top of the flashlight, walk over to the battery compartment and put in the batteries, then flip the switch to scare off the bat. Climb up the anal beads and you will encounter the Sparrow Prince.

In order to keep moving forward, you will have to defeat the Sparrow Prince first. He will be assisted by two pieces of bacteria. Defeat the bacteria first, then focus your attacks on the Sparrow Prince. He is immune to most status affects, so just do your best to whittle down his health with your most powerful attacks.

Once the Sparrow Prince is defeated, keep moving right until you come across another billiard ball. Use Nagasaki to destroy the ball, then teleport onto the bottle cap near the vibrator. Turn on the vibrator in order to clear the path to the right.

Defeat the government agents guarding the stomach, then use Jimmy's buddy ability to access the snuke. In order to disable the snuke, you will have to perform an abortion similar to the one you performed on Randy earlier in the game. Follow the onscreen prompts to diffuse the bomb. Once the bomb is diffused, Mr. Slave will cough you back out. Advance to the throne room to confront Clyde, who will force you to fight Nazi Zombie Chef.

Chef has the highest HP out of all the bosses in the game so far, so utilize your most powerful attacks. If possible, set him on fire early on to shorten the fight. When Chef utilizes his Hello Children, mash the button to prevent him from biting you. Chef will then be monetarily stunned while briefly regaining consciousness, making him vulnerable to attacks. When Chef reaches 1 HP, Clyde will set him on fire. Fart on Chef to finish him off.


text:
Star Fox: Assault/Characters

Wolf O'Donnell
The leader of Star Wolf.

Other

 * /Aparoid Queen/

title: Star Fox: Assault/Characters


text:
Playing a Video Game/Hardware

Video Game Hardware
Historically, video games have run on a variety of devices, including high powered computers, dedicated game consoles, and arcade machines. Today these remain hardware commonly used, with more common devices also gaining acceptance as gaming devices.

title: Playing a Video Game/Hardware


text:
Playing a Video Game/Replaying the Game

When replaying the game there are some approaches one can follow to increase replay value.
 * Increasing the difficulty.
 * Through In game difficulty settings.
 * Through self imposed challenges and restrictions.
 * Achievement hunting
 * Story analysis
 * Speedrunning

title: Playing a Video Game/Replaying the Game


text:
Traditional Abacus and Bead Arithmetic/Division/Dealing with overflow

Introduction
Excluding the so-called "special methods", there are two basic ways of arranging general division problems. Not knowing a standard designation for them, we have called them in the chapter: Guide to traditional division:

 * Modern division arrangement (MDA), as explained by Kojima ,

 * Traditional division arrangement (TDA), as used in ancient books like the Jinkoki (塵劫記), or the Panzhu Suanfa (盤珠算法)

MDA seems perfect for any division method; not just the modern and traditional ones, but also any of the amazing variety of methods one can imagine after reading a page like: The Definitive Higher Math Guide on Integer Long Division, and just using the beads of a 4+1 (modern) abacus. On the contrary, TDA is problematic with any division method since a collision between divisor and dividend/remainder frequently occurs, that is, both require the simultaneous use of the same column and, as this is not possible in principle, for example, in the case of modern division we would be forced to postpone the entry of the interim quotient digit in the abacus until the corresponding column be cleared by subtraction. As a result, special techniques or abaci are needed to cope with this collision. Even so, TDA has been used for centuries in conjunction with the traditional method of division while MDA seems to have been deprecated until modern times and the adoption of the modern abacus, even though MDA is the first idea that would occur to us if we tried to adapt the old division method used with counting rods (paradoxically MD!) to a single row instead of the usual three. Why? that could remain a mystery forever. However, certain advantages to TDA must be recognized:

 * It uses one rod less
 * Result does not displace too much to the left as in MDA, which is of interest in the case of chained operations. This and the above points makes TDA more suitable to small rod number abacuses, like the traditional 13-rod suanpan/soroban.
 * It saves some finger movements; for instance, in the operation 6231÷93=67 using traditional (chinese) division, one can count 14 finger movements with TDA versus 24 with MDA.
 * Hand displacements are shorter.
 * It is less prone to errors as less rods are skipped.

Are they enough to justify its historical usage?

Regarding the traditional division (Guī chúfǎ, Kijohou 帰除法) using TDA, the way to avoid the mentioned collision is to accept that the first column of the dividend/remainder, after the application of Chinese division rules, can overflow and temporarily accept a value greater than 9 (up to 18), while providing some mechanism to deal with such an overflow. This is not a problem with a traditional 5+2 or 5+3 abacus; As already explained, the additional upper beads can be used to store values as high as 20 in one column of the abacus. The problem arises when we think that 5+1 type abaci were popular in Japan during the Edo period and it seems that no ancient Japanese text explains how to deal with overflow. This is the question: What can be done on an 5+1 or 4+1 abacus?.

In a post to Soroban and Abacus Group, a member presented two examples of traditional division using an apostrophe (‘) to mark the columns or rods that temporarily received a value higher than 9 (overflow).

The apostrophe has the hindrance of breaking the vertical alignment of the columns of the abacus in the procedure tables, but let us think of this apostrophe as a typographical representation of a small 1 (¹), a bead that should be pushed, set or activated somewhere, be it on a real or imaginary column. Note that if we could open or insert a new column in the place of the apostrophe (as it is commonly done in any spreadsheet) all our problems would go away by using the new column to receive the bead, but by doing so we would be using MDA. After a short digression, three alternatives will be described below to stay on TDA.

On geeses and flocks
We will use the classical exercise 998001÷999=999 as an example to illustrate the three mentioned alternatives. This exercise is called in Chinese: The lone geese return (孤雁歸隊 Gūyàn guīduì). If you enter this division on the abacus, for instance:

and if you have an almighty imagination, no doubt, you will identify the lone bead set on K with a lone geese that has just left her flock FGH (you can see the place that she occupied in the lower part of column H). To convince her to rejoin her flock you only have to complete the division and obtain 999!

First way: Brute force
In principle, we could add the small “1” in any unused column, for example the rightmost one; but this could be annoying and inconvenient because both the hand and the attention would have to be jumping from one place to another on the abacus with the risk of ending up working in the wrong column. Here, without any further consideration, we will simply add the small "1" to the column of the just entered interim quotient digit. This may sound strange or brutal (and indeed it is), but if we can keep the value of the interim digit in memory we can operate as usual and any anomaly will disappear from the abacus in a moment. Let's see it with the  998001999=999 example on an 4+1 abacus:

On a 5+1 abacus, things are easier. We can use the 5th bead to avoid carry runs.

As we can see, we can do things this way but it does not seem like a very attractive method as we need memorization and a lot of attention to avoid making mistakes. So one should not attempt this method except as an exercise in concentration.

Second way: Suspended lower beads
If we use a 5+1, instead of pushing the bead all the way up, effectively adding the small “1” to the interim quotient digit as in the previous case, it seems more reasonable to push it only halfway, leaving a suspended lower bead as illustrated at the top of the image to the right. This suspended bead will represent the overflow while respecting the integrity of the quotient digit.

This seems like a perfect method to deal with the overflow, both in division and multiplication, everything remains under our eyes and nothing has to be memorized. In fact, when using suspended lower beads there is no need for additional upper beads, and the 5+1 abacus becomes as powerful as the 5+2  or 5+3 instruments. This might help explain why the 5+1 abacus was so popular in the past and why the 5th lower bead survived for so long. Note in the bottom half of the figure that, with some complication, this method can also be extended to the 4+1 abacus. From here on,  We will use underlined digits to represent the overflow according to the figure, since the underline reminds us of what the suspended bead looks like and they don't mess up abacus procedure tables typed with monospaced fonts as the apostrophe does.

5+1 abacus
Let us repeat the above exercise with this technique. The divisor is no longer represented and some more details are also introduced to additionally illustrate how the fifth lower bead may be used in subtraction to somewhat simplify the operation (as usual, T is 10, 1 upper bead + 5 lower beads activated)

See also division examples for illustrations of this division on 5+1, 5+2 and 5+3 type abacuses.

4+1 abacus
And now on a 4+1 abacus. We need to use the suspended group of four lower beads as a code for 9 :

If you have tried this, you have probably noticed that the group of four suspended beads behaves the same as the  suspended upper bead used on the 5+2 abacus; i.e. with "inverse arithmetic", if you move the suspended bead toward the abacus bean you are subtracting instead of adding!.

Third Way: Minimal memorization
It has been said above that using suspended lower beads seems a perfect method… but in fact it is somewhat annoying due to its inherent slowness. It is always difficult to suspend a bead, especially the small ones of modern abacus with little free space left on the rods, and this despite the silly trick of pinching the bead with two fingers and then retiring the hand as if taking a flower. It is true that with an 5+1 abacus there is no need of additional upper beads, but no doubt, if you have a lot of multiplications or divisions to do, you will prefer the speed that additional beads provide, since one very seldom need to suspend a bead on the 5+2, and never on the 5+3.

Rather than physically moving/suspending the overflow bead, it is enough to think that the bead has been already suspended on the quotient rod, or pushed on an imaginary rod flying around your abacus, around you..., or simply remember that the “overflow status” has been set to ON and that it needs to be unset back to OFF as soon as possible. This last way is similar to the process of setting flags ON/OFF in old electronic calculators programming. Obviously, moving no bead is faster than moving any bead, so nothing can be faster than this alternative. Nevertheless, we should expect to need some practice to get used to this method and prepare to make some more mistakes due to memorization. However, memorizing a digit, as in the brute force method, is worse than simply memorizing an alert condition as required here.

No need for a new example. The previous ones can be followed under this new view simply by interpreting the underlines as something like OverflowFlag: ON.

Conclusion
We have seen here three techniques to deal with overflow on 4+1 and 5+1 abacuses that pushes the small “1” up on the interim quotient column:

 * 1) All way, effectively adding it as a carry to the quotient
 * 2) Only half way, leaving a suspended lower bead
 * 3) Nothing at all (but in our minds)

These methods bring us the possibility of using traditional techniques and arrangements on any abacus type by simply adapting the mechanics to the presence/absence of additional beads. This is an advantage if you finally end up convinced by traditional techniques.

It has been mentioned that no ancient Japanese text explains how to deal with overflow with a 5+1 abacus. Most likely the form used was one of the last two methods introduced here. Consider that the second method can be demonstrated to others in just seconds, and that once seen, it is neither forgotten nor requires further explanation; It is so obvious. So there is not much need to write long texts to convey that knowledge.