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MathNet 2026 — Part 06 Question 90

Math Olympiad Vault · MathNet 2026 — Part 06

Question 90

The equation $AB \times CD = EFGH$, where each of the letters $A, B, C, D, E, F, G, H$ represents a different digit and the values of $A, C$ and $E$ are all non-zero, has many solutions, e.g. $46 \times 85 = 3910$. Prove that the largest value of $EFGH$ for which there is a solution, is $72 \times 95 = 6840$.