# data[].attributes.attachment_link.description
You have to make sure you start by moving 2 circles forward then you always make sure your number of moves and the computer's number of moves sums up to 6 and you will win.

# data[].attributes.attachment_link.readable_text
Imagine that round the back of where you live is a piece of ground that your family want to change. Instead of grass or plants growing there you want to have a patio. To prepare to change it the ground is dug up and levelled, it is then measured and found to be a square $10$ by $10$ [this could be feet, metres or yards it does not really matter for this challenge]. You then go to a large store that sells tiles to go on the ground. To your surprise you find that they sell tiles in ten different sizes; $1$ by $1$, $2$ by $2$, $3$ by $3$, etc. up to $10$ by $10$. You decide to go back home for a while and work a few ideas out.

You start by drawing a $10$ by $10$ square; and then you think about what sizes of tiles to use to cover it.

If you use $1$ by $1$ tiles then you find [or know already!] that you will need $100$ of them. So your shopping list would look like :-

$100$ tiles @ $1$ by $1$ > Total number of tiles $100$

If you use $10$ by $10$ tiles then you find [or know already!] that you will need 1 of them. So your shopping list would look like :-

$1$ tiles @ $10$ by $10$ > Total number of tiles $1$

If you use $2$ by $2$ tiles then you find [or know already!] that you will need $25$ of them. So your shopping list would look like :-

$25$ tiles @ $2$ by $2$ > Total number of tiles $25$

You could of course use a mixture of different sized tiles.

If you use $12$ tiles $2$ by $2$ and $4$ tiles $3$ by $3$ and $1$ tile $4$ by $4$ your shopping list would look like :-

$12$ tiles @ $2$ by $2$
$4$ tiles @ $3$ by $3$
$1$ tile @ $4$ by $4$ > Total number of tiles $17$

So you could, with these examples use $1, 17, 25$ or indeed $100$ tiles.

Your challenge starts by asking you to try to find lots of different numbers of tiles that could be used to cover this $10$ by $10$ patio.

You could think about the artistic appearance of it as well if you like. However all the patio must be covered and no cutting any of them to make different sizes or shapes ... they're actually very, very hard to cut anyway.

You could now think about these kinds of questions and perhaps you would think of other questions of your own to pursue.

1. Are there some numbers of tiles used that actually are made up of different mixtures of tiles? [For example in our one that used $17$, could you get to use just $17$ tiles but they require a different shopping list from the one above?]

2. Are there some numbers between $1$ and $100$ that cannot be used as the total number of tiles required?

3. Is there some system for getting new examples that use different numbers of tiles?

You might then think about how all this might or might not change if the patio had been $9$ by $9$ [$8$ by $8$, $7$ by $7$ etc ...]

Well good luck, and if you're artistically inclined I guess that you may have some results that would look really good displayed. Since you're sitting at a computer it may be that you could use a "draw/art" package to do all the work on the screen for you. But have a break from the screen every hour ... your body deserves it!

# data[].attributes.attachment_link.description
Imagine that round the back of where you live is a piece of ground that your family want to change. Instead of grass or plants growing there you want to have a patio.

# data[].attributes.attachment_link.description
Try a few examples. Can you explain why your answer is always a multiple of 11?

# data[].attributes.attachment_link.description
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

# data[].attributes.attachment_link.readable_text
This is a really interesting problem from NRICH. Please visit their site to find many more rich and engaging math tasks.

Remember that you can try this not only on paper but using coins or other objects around you. As long as you can tell the sides from each other, you can use it!

Reference

The NRICH website publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers' Resources for use in the classroom.

# data[].attributes.attachment_link.description
This is a really interesting problem from NRICH. Please visit their site to find many more rich and engaging math tasks. Remember that you can try this not only on paper but using coins or other objects around you. As long as you can tell the sides from each other, you can use it!