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UKMT Senior Kangaroo, 2025

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. What is the sum of the answers to the clues for 1 ACROSS, 3 ACROSS and 5 ACROSS? ACROSS 1. A factor of 1221. 3. A multiple of 17. 5. A prime. DOWN 1. A factor of 1221 different from 1 ACROSS. 2. A cube. 4. A prime.

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