There are 10 coins laid out on a table in a straight line

* * * * * * * * * *
1 2 3 4 5 6 7 8 9 10

The goal is to get 5 stacks of 2 coins each in only 5 jumps.
A coin must jump over exactly 2 other coins and land on a third.
Coins may jump in either direction.

Example:
Jump 1: Jump coin 10 on top of coin 7.
Jump 2: Jump coin 8 on top of coin 6. This is possible since coin 7 and 10 now form a stack of two coins.

Apparently, there is a solution for every string of 2N coins, whenever N >=4, and no other.

The eight string plays a role in the solution to this problem (5,2), (3,7), (1,4), (8,6).

We produce a solution for the 2N+2 string from the solution for the 2N string by tacking on (2N-3,2N) right at the beginning.

We show the non-existence of solution for 2,4 and 6 strings by inspection. 

Posted by FrankM on 2008-03-13 12:26:47