I have found the following card trick:
- Take a stack of n cards, with a known order.
- Deal the cards from your hand onto the table like this: Card from the top, then card from the bottom, from the top, from the bottom, etc until the deck is depleted.
- Keep dealing the cards like this. After a certain amount of deals (lets call that d) the original order will be restored.
I have made a table for n=1 through 25. The numbers for d are, consecutively:
I'm trying to find a pattern here, but I can't find one. My first thought was that after the same amount of deals as the amount of cards the sequence would repeat. Some seem to conform to n-1=d, but most don't. If you check for n-1=z*d, where z is an integer, most of them conform, but some don't.
Does anyone know what logic is hidden here? What is so special about n=16 and 17 (both just 5 deals required) and n=22 (just 7 deals required)?