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Daily puzzle · 2026-10-28 · Divisibility

Mathbound Daily Puzzle — 2026-10-28 — Divisibility Solution

Level 3

How many pairs of positive integers (x,y)(x,y) with x≤yx\le y satisfy 1x+1y=121\dfrac1x+\dfrac1y=\dfrac1{21}?
  1. A.5
  2. B.9
  3. C.6
  4. D.21
  5. E.4

Answer: A

Key idea: (x−t)(y−t)=t2(x-t)(y-t)=t^2.

Set it up: Divisors d≤td\le t of t2t^2.

Solution: 55.

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Mathbound Daily Puzzle — 2026-10-28 — Divisibility Solution