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?