# 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:

- 3, 2, 1
- 1, 3, 2
- 2, 1, 3

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.

## 13 December

There are 6 ways to split the sequence of the numbers 1 to 5 into three shorter sequences:

- 1 and 2 and 3, 4, 5
- 1 and 2, 3 and 4, 5
- 1 and 2, 3, 4 and 5
- 1, 2 and 3 and 4, 5
- 1, 2 and 3, 4 and 5
- 1, 2, 3 and 4 and 5

Today's number is the number of ways to split the sequence of the numbers 1 to 10 into five shorter sequences.

## 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?