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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

Seventy pupils (37 boys and 33 girls) are divided into two groups, with forty pupils in Group 1 and 30 pupils in Group2. How many more boys are there in Group 1 than there are girls in Group 2?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. 

This problem is taken from the UKMT Mathematical Challenges.
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