Owlet puzzle #47
Released Friday, August 21, 2026 UTC
33
the answer for puzzle #47
The five clues
- A two-digit multiple of 11.
- It is odd but not prime.
- The sum of its digits equals 6.
- It is the largest number that is not the sum of distinct triangular numbers.
- It is the atomic number of arsenic.
Backstory
33 = 3 · 11 was, for decades, one of only two positive integers under 100 not of the form 9k ± 4 for which no representation as a sum of three integer cubes was known. Andrew Booker cracked it in 2019 with 33 = 8,866,128,975,287,528³ + (−8,778,405,442,862,239)³ + (−2,736,111,468,807,040)³; shortly after, Booker & Sutherland resolved 42, the last holdout under 100. Numbers ≡ ±4 (mod 9) cannot be sums of three integer cubes at all, so the search space is restricted from the outset.
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