Owlet puzzle #52
Released Wednesday, August 26, 2026 UTC
145
the answer for puzzle #52
The five clues
- A three-digit multiple of five below two hundred.
- A three-digit multiple of five whose digits sum to ten.
- A three-digit factorion.
- It is not prime; it factors as 5 times 29.
- One of only four numbers (with 1, 2, 40585) equal to the sum of the factorials of its digits.
Backstory
145 = 1! + 4! + 5! = 1 + 24 + 120. Such numbers are called factorions; there are only four in base 10: 1, 2, 145, and 40585. The count is finite because factorials grow much faster than digit-sum bounds allow. 145 is also the tenth pentagonal number, P(10) = 10·(3·10 − 1)/2, and it splits as a sum of two squares in two distinct ways: 145 = 12² + 1² = 9² + 8².
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