Only doors whose numbers have an odd number of factors will remain open. The only numbers that have that property are perfect squares. Back to problems Card-shuffling machine Solution to this problem was provided by Chris Shannon. Let's assume that after the first shuffle the ace was in the second slot. To see why this is the case look at the diagram below.
Same logic applies to all other slots.
If we assume ace to be in any other slot after the first shuffle, we will eventually get two cards that must go into the same slot. Three piles Solution to this problem was provided by Fernando Colus. Put the last 9 weights aside for a moment. Now, each of 332 groups can be easily divided into three equally-weighted piles. Back to problems 20 cubes Solution to this problem is coming soon.