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.
Note: You may place the initial checkers anywhere you wish, as necessary.
(In reply to
re(2): Thoughts... by DJ)
DJ, you said to create the arrangement needed for level 3, but one unit higher. I know that's what I need to do, but I don't see how to do it. Getting 5 checkers across on level 1 can be done a number of ways, but then how do I get 3 across on level zero beneath them? Call it mental block, but I'm just not seeing it.
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Posted by Bryan
on 2003-06-26 05:19:26 |
re(3): Thoughts...
