It’s been almost a year since Bill Gasarch gave us the problem of four-coloring the nodes of a 17 × 17 grid in such a way that no rectangle has all four corners the same color. (See my earlier commentary here and here.)
The problem remains open, the prize of $172 unclaimed.
A few weeks ago I had a momentary fantasy that I might have come upon the answer. I was browsing in a strange New England emporium called Building 19, full of merchandise found nowhere else (thankfully). From across the room I spotted a sofa cushion that looked like it might well be a rectangle-free four-colored grid.
Sadly, a closer look showed that the cushion is neither rectangle-free nor four-colored. Nor 17 × 17 for that matter. And the price tag reads $399.90, so if Bill wants to receive the solution in the form of tacky furniture, he’s going to have to up his offer.
On the other hand, the hardest level (“Ninja”) in Schweitzer’s game is only a 12 × 12 array, so don’t think you’re going to click away at little colored squares and earn yourself $289.
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