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UKMT Junior Mathematical Olympiad, 2025

Number theory Difficulty 2.0 Junior Prove it United Kingdom

The code for my bank card is a four-digit integer. No digit is zero. The first digit is twice the third digit. The fourth digit is three times the second digit. The four-digit integer is a multiple of 9. What is the code for my bank card?

This is an Olympiad problem, so you must also explain why no other solution is possible.

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