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.
Starting with 5 piles of 2, I first tried 22222 > 1212121, but realized that one side or the other there'd be a single coin left unable to jump.
But 22222 > 1211212 (going in opposite directions from the second and third stack) and then to 11111212 and from there to 111111112 and then 1111111111. Then place them in reverse order:
1111111111
111111 112
111 11 212
121 1 212
22 2 2 2
The last is two steps combined into one (1>3 and 9>5). Also, instead of 9>5, we could have done 5>9.
Overall this is 7>10, 4>8, 6>2, 1>3 and (9>5 or 5>9), and the last two moves could be done in either order (that is, the 9>5 or 5>9 could come before the 1>3).
Edited on October 18, 2004, 3:54 pm

Posted by Charlie
on 20041018 15:49:22 