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PostPosted: Thu Mar 07, 2013 10:32 am 
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Joined: Thu Feb 28, 2013 1:49 pm
Posts: 12
Hi all

Any help to work out the following really appreciated:

You have 250 1cm2 square tiles which are either red or blue. There are enough 1cm2 square tiles of each colour to make up a larger square where both diagonals are made up entirely of blue square tiles. If you made up the largest possible square how many blue 1cm2 square tiles would you need along the diagonals?

Answer- 29 blue tiles
Many thanks


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PostPosted: Thu Mar 07, 2013 10:47 am 
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Joined: Mon Aug 22, 2011 8:20 pm
Posts: 1706
Location: Warwickshire
Start by thinking about what the largest square you can make is.
Square numbers:
1x1 = 1
2x2 = 4
...
10x10 = 100
...
14x14 = 196
...
etc
You need the largest one which is still less than 250.

The number of squares on each diagonal will be related to the length of each side. But think about whether any of those squares will be double counted? Clue: think about a square where the length of each side is an odd number, and another where it is an even number? Does it make a difference?

Try to work it out using this method.

If you still can't see it highlight the space between the asterisks to reveal more!

*****
15x15 = 225
16x16 = 256
So the square is 15x15 - meaning 15 squares on each diagonal.
But the centre one of these will be the same square - so (15 * 2) - 1 = 29 blue tiles.

*****


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PostPosted: Thu Mar 07, 2013 10:57 am 
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Joined: Thu Feb 28, 2013 1:49 pm
Posts: 12
Thanks Okanagan, I did start the same way, but complicated it myself with the Pythagoras theorem :?
I liked your challenge- that refreshed me.

Regards


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