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UKMT Senior Kangaroo, 2021

Number theory Difficulty 2.0 Junior Prove it United Kingdom

Each cell in this cross-number can be filled with a non-zero digit such that all of the conditions in the clues are satisfied. The digits used are not necessarily distinct. What is the answer to 2 DOWN? The grid is a 3 by 3 arrangement of cells: row 1 has cell 1 (top-left), cell 2 (top-middle), and a shaded cell (top-right); row 2 has cell 3 (labelled, left), a blank cell (middle), and cell 4 (labelled, right); row 3 has a shaded cell (left), cell 5 (labelled, middle), and a blank cell (right). ACROSS: 1. A prime which is the sum of two squares. 3. Twice the answer to 2 DOWN. DOWN: 1. $p \times q$ , where $p, q$ are prime and $q = p + 4$ . 4. 60% of 5 ACROSS.

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