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April 2015

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A few years ago (https://www.research.ibm.com/haifa/ponderthis/challenges/July2007.html), we posted a challenge about building a fence to prevent viewing through a square property.

This month's challenge is a three-dimensional discrete version of the same problem. The optimal solution for the two-dimensional discrete version is

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WPPPPP
WPPPPP
WPPWWW

The trivial way to extend it to three dimensions is to have two opposite faces full of Wendies and the other four half filled. Tweaking a little, we get 170 Peter Pans:

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WWWPPPWPPPPPPWPPPPPPWWPPPPPWWPPPPPPWPPPPPPWPPWWWW
WWWPPPWPPPPPPWPPPPPPWWPPPPPWWPPPPPPWPPPPPPWPPWWWW
WWWPPPWPPPPPPWPPPPPPWWPPPPPWWPPPPPPWPPPPPPWPPWWWW
WWWPPPWPPPPPPWPPPPPPWWPPPPPWWPPPPPPWPPPPPPWPPWWWW
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW

The best solution that we know of has 172 Peters, which requires some Wendies in the inner 5x5x5 cube:

WWWWWWWWWWWWWWWWWWWWWWWWPWWWWWWWWWWWWWWWWWWWWWWWW
WWWWPPWPPPPPPWPPPPPPWPPWPPPPWPPPPPPWPPPPPPWPPWWWW
WWPWWPWPPPPPPWWPPPPPPPPPPPPWPPPPPPWWPPPPPPWPWWPWW
WWWWPPWPPPPPPWPPPPPPWPPPPPPWWPPPPPPWPPPPPPWPPWWWW
WWPWWPWPPPPPPWWPPPPPPPWPPPPPPPPPPPWWPPPPPPWPWWPWW
WWWWPPWPPPPPPWPPPPPPWPPPWPPPWPPPPPPWPPPPPPWPPWWWW
WWWWWWWWWWWWWWWWWWWWWWWWPWWWWWWWWWWWWWWWWWWWWWWWW

And thanks to LaurV for the interesting discussion on the Mersenne forum http://www.mersenneforum.org/showthread.php?t=20151.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com