Owlet puzzle #95
Released Thursday, October 8, 2026 UTC
729
the answer for puzzle #95
The five clues
- A three-digit odd perfect square.
- A perfect square AND a perfect cube.
- Divisor count is 7 (unusually few for a three-digit number); in base 3 it's a single 1 followed by zeros.
- The number of unit cubes filling a 9-by-9-by-9 cube.
- Its base-3 representation is 1000000.
Backstory
729 = 3⁶ = 27², both a perfect square and a perfect cube — indeed a sixth power. The smallest such rendezvous is 64 = 8² = 4³; 729 is the next, and the pattern continues at 4096 = 2¹², 15625 = 5⁶, and so on. Every sixth power is simultaneously a square and a cube.
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