The Thirty-Three Pearl Necklace
A merchant's pearl necklace has 33 pearls, with the single largest, most valuable pearl set exactly in the middle. Counting from one end toward the middle, each pearl costs £100 more than the pearl before it. Counting from the other end toward the middle, each pearl costs £150 more than the one before it. The whole necklace is valued at £65,000 — what is the middle pearl worth?
Reveal the answer
£3,000. If the middle (17th) pearl is worth M, the 17 pearls counted in from each end (sharing that middle pearl) sum to 17M − 13,600 and 17M − 20,400; removing the double-counted middle pearl gives 33M − 34,000 = 65,000, so M = 3,000. It's Puzzle No. 99 in Henry Dudeney's 1917 Amusements in Mathematics, one of his many arithmetic chains dressed up as a jewelry riddle.
— Henry Dudeney, Amusements in Mathematics — Puzzle No. 99, 'Various Arithmetical and Algebraical Problems,' 1917
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