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?

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Chess

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?

Squares in Rectangles

Age 11 to 14 Challenge Level:

A $2$ by $3$ rectangle contains $8$ squares. Can you see how?

A $3$ by $4$ rectangle contains $20$ squares. Can you see how?

A $4$ by $6$ rectangle contains $50$ squares. Can you see how?

What size rectangle contains exactly $100$ squares?

Is there more than one?
Can you find them all?
Can you prove that there are no more?