IBM Ponder This #219 · July 2016

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.

Solution

Best opened after a real attempt

To be added.