916238457 is a nine-digit number that has the property that has the digits 1 to 9 exactly once and the digits 1 to 5 are in counting order but the digits 1 to 6 are not. How many such numbers are there?

I have a very large plot of land on which I have stacked bales of hay, each measuring 1m x 1m x 1m. They are stacked 10 bales high, and span a couple thousand wide and deep. To keep them out of the weather I have also placed a tarp on top that cannot be [...]

A class has six pairs of twins. The teacher wishes to set up teams for a quiz, but doesn’t want to put any pair of twins in the same team.

1) In how many ways can they be split into two teams of six?

2) In how many ways can they be split into three teams of [...]