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UKMT Senior Kangaroo, 2024

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

Each cell in this cross-number can be filled with a non-zero digit so that all of the conditions in the clues are satisfied. The digits used are not necessarily distinct.

ACROSS
1. A prime.
3. The answer to this Kangaroo question.
5. Shares a two-digit common factor with 1 DOWN.

DOWN
1. The sum of two different sixth powers.
2. 101 less than a square number.
4. The sum of all the digits in this crossnumber, once correctly completed.

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