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UKMT Junior Mathematical Olympiad, 2026

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the following sum, the letters $Y$ , $U$ , $M$ and $S$ stand for single digits.

$\overline{YUMS} + \overline{YUM} = 2026$

(a) Find one possibility for the values of $Y$ , $U$ , $M$ and $S$ . Only the answer is required.
(b) Prove that this is the only possible solution. A full explanation is required.

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