Owlet puzzle #122
Released Wednesday, November 4, 2026 UTC
429
the answer for puzzle #122
The five clues
- A three-digit multiple of thirty-three.
- A three-digit product of three distinct primes.
- A three-digit Catalan number — C₇.
- Equal to 3 · 11 · 13.
- The number of ways to triangulate a convex nonagon.
Backstory
429 = C₇ = 3 · 11 · 13, the seventh Catalan number. It counts Dyck paths of length 14, binary trees with 7 internal nodes, and non-crossing chord diagrams on 7 chords. The Catalan sequence begins 1, 1, 2, 5, 14, 42, 132, 429 — appearing in over 200 combinatorial contexts documented by Stanley.
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