Tag Archives: logic games

Flipping the Glasses

In the last post, I mentioned a simple logic puzzle that I’d stumbled over while wandering around the interweb. Start with four glasses, in a row, all upright. The goal is, through a series of moves, to turn them all upside down. On each move, you flip three of the four glasses — up if down or down if up.

The goal is to end up with all four glasses upside-down in the least number of moves possible. It’s not hard to find the solution by trial and error, but it turns out there’s an underlying trick that not only solves it but solves it regardless of the number of glasses (where each move flips N-1).

Bonus: these solutions even look pretty — or at least symmetrical.

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Square Logic

Or do I mean Logic Square? Because it works either way. The Logic Square (or Square Logic) in question is a logic game created by Charles Lutwidge Dodgson (1832-1898) and introduced in his 1896 book Symbolic Logic Part I (a second part was published posthumously).

Dodgson was a capable mathematician, but most probably know him by his penname, Lewis Carroll, under which he wrote poetic fantasy fiction about a girl who goes on wild adventures.

But this is about his logic game. It’s like a square Venn diagram with game pieces.

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