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Puzzles

21 December

There are 3 ways to order the numbers 1 to 3 so that no number immediately follows the number one less that itself:
Today's number is the number of ways to order the numbers 1 to 6 so that no number immediately follows the number one less that itself.

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13 December

There are 6 ways to split the sequence of the numbers 1 to 5 into three shorter sequences:
Today's number is the number of ways to split the sequence of the numbers 1 to 10 into five shorter sequences.

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18 December

Today's number is the maximum number of pieces that a (circular) pancake can be cut into with 17 straight cuts.

15 December

If the numbers 1 to 7 are arranged 7,1,2,6,3,4,5 then each number is either larger than or a factor of the number before it.
How many ways can the numbers 1 to 7 be arranged to that each number is either larger than or a factor of the number before it?

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