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Puzzle 1
How many squares of any size on this chessboard do not contain a rook?
Reasoning There are 61 squares of size 1 x 1. There are 37 squares of size 2 x 2. There are 15 squares of size 3 x 3. There are 3 squares of size 4 x 4.
Giving a total of 61 + 37 + 15 + 3 = 116 squares.
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Puzzle 2
Last week, I travelled from Birmingham to Glasgow, the long way round (on a bicycle!).
On the first day, I travelled one quarter of the distance.
On day two, I travelled one half of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one third of the remaining distance.
I now have 21 miles left to travel.
How far is it from Birmingham to Glasgow in total?
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