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Chessboard squares

It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths IX,
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Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

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