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Puzzles

20 December

There are 6 different ways that three balls labelled 1 to 3 can be put into two boxes labelled A and B so that no box is empty:
How many ways can five balls labelled 1 to 5 be put into four boxes labelled A to D so that no box is empty?

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22 December

There are 12 ways of placing 2 tokens on a 2×4 grid so that no two tokens are next to each other horizontally, vertically or diagonally:
Today's number is the number of ways of placing 2 tokens on a 2×21 grid so that no two tokens are next to each other horizontally, vertically or diagonally.

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24 December

There are six ways to put two tokens in a 3 by 3 grid so that the diagonal from the top left to the bottom right is a line of symmetry:
Today's number is the number of ways of placing two tokens in a 29 by 29 grid so that the diagonal from the top left to the bottom right is a line of symmetry.

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6 December

There are 12 ways of placing 2 tokens on a 2×4 grid so that no two tokens are next to each other horizonally, vertically or diagonally:
Today's number is the number of ways of placing 5 tokens on a 2×10 grid so that no two tokens are next to each other horizonally, vertically or diagonally.

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