Assume you have a checker board with 7 rows and infinite columns. You can place checkers on only the first 2 rows initially (number these -1 and 0). Then you may jump other checkers up, down, right, and left but not diagonally. The goal is to get as high a row as possible. For example you can get to the second level with four checkers like this:
Level Setup Turn 1 Turn 2 Turn 3
------ ------- ------- ------- -------
2 ····· ····· ····· ···a·
1 ····· ···d· ···d· ·····
0 ·abc· ·ab·· ···a· ·····
-1 ···d· ····· ····· ·····
It turns out you need at least 2 checkers to get to level 1, 4 to get to level 2, 8 to get to level 3, and 20 to get to level 4.
Prove the least number of jumps it would take to get to level 5, and how you would do it.
: You may place the initial checkers anywhere you wish, as necessary.
(In reply to Impossible?
It's not impossible you need 20 peices to get to level 4 I worked that one through and it works, 5 is harder and I did it but I'm trying to find the lowest number of attempts. You can jump pieces over each other on the back lines i.e. in the same line 0 to 0 and remove the piece you jumped off the board. level four isn't very hard, why so much trouble with it. DJ maybe you can show a worked solution, showing twenty moves in the style posed in the question is a bit long.
Posted by Yoseph
on 2003-08-20 08:35:58