Owlet puzzle #121
Released Tuesday, November 3, 2026 UTC
365
the answer for puzzle #121
The five clues
- A three-digit multiple of five under 400.
- A three-digit count often quoted for a full annual cycle.
- Equal to 5 × 73.
- Equal to a sum of three consecutive squares (10² + 11² + 12²) AND also to a sum of two consecutive squares (13² + 14²).
- Equals 10² + 11² + 12², and also 13² + 14².
Backstory
365 = 10² + 11² + 12² = 13² + 14² has two distinct representations as sums of consecutive squares — a Diophantine coincidence. Its factorization is 5 · 73, and 365 days give the solar year to within a leap-day correction every four years.
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