Owlet puzzle #30
Released Tuesday, August 4, 2026 UTC
24
the answer for puzzle #30
The five clues
- A two-digit number with eight or more divisors.
- The number of hours in a day.
- The smallest positive integer with exactly eight divisors.
- Equal to 4! and 2³·3.
- Also the order of the symmetric group S₄ and the largest factorial below one hundred.
Backstory
24 hours per day, 4! = 24, and |S_4| = 24 permutations of four objects. The 24-cell is a regular polytope in 4D with no analogue in any other dimension, and 1²+2²+…+24² = 70² is the only nontrivial cannonball stack (Watson, 1918).
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