July 2016

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Ponder This Challenge:

This month's challenge is in honor of the late Professor Solomon Golomb (https://en.wikipedia.org/wiki/Solomon_W._Golomb), who received the National Medal of Science from President Obama on February 2, 2013. Prof. Golomb received his award in the same ceremony as Rangaswamy Srinivasan from IBM, who was awarded his medal for contributions to laser eye surgery.

Golomb proved that any 2^Nx2^N board with a missing square can be tiled with a single r-shaped tromino.

Find at most three types of pentominos (http://mathworld.wolfram.com/Pentomino.html) that can tile every 4^Nx4^N board with a missing square.

Prove your solution.

Update (3/7):

Your pentominos should be able to tile all the 4^N*4^N boards with any possible missing square. You can use free pentominos (rotation and reflections are allowed). Solving with less than three pentominos types will earn you a '*'.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

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