W-0093

A superpermutation on 12 symbols, found by Jay Pantone. It beat the previous record W-0091 by 2 letters and was the record on Nov 9, 2026. The next record W-0096 beat it by 9 letters.

Length: 522,736,501
Repeated permutations: 177,378
Received: Nov 9, 202618:32:41 UTC

Begins

0123456789AB0123456789A0B123456789A01B23456789A012B3456789A0123B456789A01234B56789A012345B6789A0123456B789A01234567B89A0…

Windows

	522,736,490	windows of 12 consecutive letters
=	479,001,600	distinct permutations
+	177,378	repeated permutations
+	43,557,512	windows that are not permutations

Detours by weight

A step is the move from one permutation in the superpermutation to the next permutation in it, and its weight is the number of letters added in that move. A detour starts at a step that differs from the next step of the recursive construction, and ends at the first permutation after that whose next step has weight 1. The weight of a detour is the number of letters added in it. After each detour, we consider the recursive construction to begin again from scratch at the permutation where the detour ends.

Weight	Detours
1	0
2	0
3	1,065,448
4	459
5	550
6	1,081
7	33
8	24
9	31
10	23
11	7
12	0

How it was found

From the submitter

This word is William Echols's 522,736,503-letter word with its pieces reordered. I cut it at every step of weight 4 or more, where no permutation window crosses, and Gurobi found the order of the pieces with the most overlap between neighbors. That saved 2 letters, and no other order of these pieces is shorter.

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Learn about the Detour file format

Download Detour (.detour) 41.6 kB, or 522.7 MB decoded