|Is it possible to fill each square of a 5x5 grid with either a 1 or a 0, such that every 2x2 square is unique? The example has one repeated square.|
Source: Original. Found later as a color-map question in Aaron J. Friedland's book Puzzles in Math & Logic (New York, 1970) on pages 9-10 and 44.
There are 800 solutions for the problem as stated. Several solvers noticed the problem could actually be solved as a 4x4 grid, allowing for wrapping at the sides and top/bottom (equivalent to saying the first and last rows and columns above are the same.) Neglecting rotations, reflections, 0-to-1 inversions, and cycles, there is only one such solution. Yaacov Yoseph Weiss provided it first:
0001 0010 1011 0111