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Counting Langford pairings for 31 and 32 pairs

Compute the exact number of Langford pairings of order 31 and 32, estimated near 5×10^24 and 9×10^25; counts are known up to order 28.

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1{
2 "domain": "computer-science",
3 "topics": [
4 "constraint-programming",
5 "algorithms-complexity"
6 ],
7 "type": "algorithm",
8 "source": {
9 "key": "csplib",
10 "name": "CSPLib",
11 "url": "https://www.csplib.org/Problems/prob024/",
12 "id": "prob024",
13 "curator": "CSPLib editors",
14 "poser": "Toby Walsh",
15 "status": "open",
16 "as_of": "2026-10-20",
17 "catalog": "0521c19bbd38"
18 },
19 "review": true,
20 "approval": "first-time"
21}