Owlet puzzle #31
Released Wednesday, August 5, 2026 UTC
142857
the answer for puzzle #31
The five clues
- A six-digit multiple of nine, digit sum twenty-seven.
- A six-digit number equal to R₆/7, where R₆ = 999999.
- The digits are exactly the set {1,4,2,8,5,7} — the same as 1/7 in decimal.
- Multiply it by 2, 3, 4, 5, or 6 and you get a cyclic permutation of itself.
- One-seventh of 999999 — the six-digit repunit R₆.
Backstory
142857 is the smallest cyclic number in base 10, arising from 1/7 = 0.142857142857… Its multiples 1×, 2×, …, 6× are all rotations of the same six digits, and 142857 × 7 = 999999. It equals (10⁶ − 1)/7; every full-reptend prime yields a longer cyclic number the same way.
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