Owlet puzzle #79
Released Tuesday, September 22, 2026 UTC
9999
the answer for puzzle #79
The five clues
- A four-digit palindrome.
- The sum of its digits is at least twenty.
- All four of its digits are the same.
- Its digit sum is a perfect square.
- 10⁴ − 1 factors cyclotomically as 9 · 11 · 101, giving a reciprocal with period 4: 0.00010001…
Backstory
9999 = 3² · 11 · 101 = 10⁴ − 1 = (10²−1)(10²+1) = 99 · 101. It's the largest four-digit number, and 1/9999 has repeating period 4: 0.00010001... — reflecting the factorization 9999 = φ₁(10)·φ₂(10)·φ₄(10) over cyclotomic polynomials at 10.
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