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IMSO 2025 Mathematics — International Short Answer Question 24

IMSO Maths · IMSO 2025 Mathematics — International Short Answer

Question 24

Let $\overline{IM}$ and $\overline{SO}$ be both two-digit prime numbers, where I, M, S and O are distinct digits. Re-arranging the digits, we form a new four-digit number $\overline{OSMI}$, which is even and divisible by 9. What is the difference between the largest and the smallest possible values of $\overline{OSMI}$?