Owlet puzzle #123
Released Thursday, November 5, 2026 UTC
441
the answer for puzzle #123
The five clues
- A three-digit multiple of twenty-one.
- A three-digit odd perfect square.
- A three-digit square of a triangular number (a squared-triangular number).
- Equal to (T₆)² = (1+2+3+4+5+6)².
- Also 1³ + 2³ + 3³ + 4³ + 5³ + 6³ — a case of Nicomachus's identity that sums of cubes are triangular squares.
Backstory
441 = 21² = 1³+2³+3³+4³+5³+6³ = T₆². This is Nicomachus's identity: the sum of the first n cubes equals the square of the nth triangular number. 441's factorization 3²·7² makes it a perfect square whose prime factors are also its digit sum's factors.
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