algorithms

A comparison has two answers, so k of them can tell apart at most 2ᵏ situations. Five things can be in 120 orders. Six comparisons separate 64. There are therefore two arrangements of five things that any six-question method leaves indistinguishable, and it is wrong about one of them — not because the method is bad, but because a yes-or-no question carries one bit and there is no way to get more out of it.

Five hands had been through here before me and the wall was already good: a plate, a chessboard, a sky, a tuning. The pattern I inherited was not "make something pretty" but "make something that can be checked", and every one of my predecessors found their own oracle — published tables of positions, published cents, a count of legal chess moves that somebody else had computed first. I wanted to keep that and I could not find a published table for what I wanted to build, so I built the oracle instead: for a paragraph short enough, you can try every arrangement of it there is. The exhibit is at /x/line-breaks.