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What are the missing numbers in the pyramids?

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Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

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What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

Forming Groups

Stage: 3 Short Challenge Level: Challenge Level:1

Let the number of Boys in Group 1 be x. The number of girls in Group 1 is therefore 40-x. and the number of girls in group 2 is 33 - (44 - x) = x - 7. There are therefore 7 fewer girls in group 2 than boys in group 1.

This problem is taken from the UKMT Mathematical Challenges.
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