## 'Coded Hundred Square' printed from http://nrich.maths.org/

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Class 3 from Selside Endowed C of E Primary wrote to say:

We began by working out that the number represented by three symbols must be $100$. This jigsaw piece helped us to identify other symbols. We identified that $1$ was represented by a large diamond and quickly found the opening jigsaw piece for the hundred square. By using the patterns of the hundred square we were able to complete it without much difficulty.

Ilakya from Glenarm College used a similar method and said:

Here is how I figured the code out:
First I started with one hundred as it has three digits. I found the code with three shapes and put it in the place of one hundred.
Now I realized that in one row all the shapes except the last shape must start with the same shape because numbers apart from $1$-$9$, in one row start with the same number. e.g. $11$, $12$, $13$, $14$, $15$, $16$, $17$, $18$, $19$.
All these numbers start with $1$ so they all must start with the same shape. If I could not figure out where in that row the shape should go I looked at the last number.
In one column all the last numbers should be the same. e.g. $11$, $21$, $31$, $41 ,$51 , $61$, $71$, $81$, $91$.
All these numbers all end in $1$ and are in the same column so therefore must be represented by the same shape. By using this technique I built the whole hundred square!

Sophie and Kyle from Holy Cross Primary explained clearly their way of working:

First we noticed the only piece with three symbols had to fit in to the $100$ slot.
From that you can tell the big diamond is the symbol for $1$ and the small diamond is the symbol for $0$.
With this information we placed the number $1$ piece in to the right position.
With this piece in place it gives you the symbols for $2$, $3$, $4$, and $5$. We then put in the single symbols in to place at the top using our information.
Knowing the symbols for $0$ - $9$ it was a simple case of putting the rest of the pieces in to place.

Students from Newmarket College sent in very good reasoning too. They also sent in this image of the completed square:

Eloise went about the problem slightly differently:

My solution is each piece has a code on it so I started with the single symbols (the ones with one symbol on it) then found out that when I put the single symbols that I found out the numbers that matched with the different symbols so then the rest of the pieces just fell in place.

Robbie from Orchard Junior School worked in a similar way to Eloise.

Kyle form Orchard Junior School used a different approach:

I worked out that the diamond was $1$ because it was the only symbol that apeared $11$ times in the solution and that the smaller diamonds were $0$ because it was the only symbol that apeared $12$ times which made the rest easy.

I like this way of working, Kyle, but are you sure that the number $1$ only appears eleven times?
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