Owlet puzzle #3
Released Wednesday, July 8, 2026 UTC
496
the answer for puzzle #3
The five clues
- A three-digit multiple of sixteen.
- Its proper divisors sum to itself.
- It is a perfect number, only the third one.
- Its divisors are 1, 2, 4, 8, 16, 31, 62, 124, 248.
- It equals 2⁴·(2⁵−1), Euclid's perfect-number form.
Backstory
496 = 2⁴ · (2⁵ − 1) is the third perfect number, after 6 and 28. The Euclid–Euler theorem says every even perfect number has the form 2^(p−1)·(2^p − 1) whenever 2^p − 1 is prime; here p = 5 gives the Mersenne prime 31.
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