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UKMT Pink Kangaroo, 2021

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Tatiana's teacher drew a $3 \times 3$ grid on the board, with zero in each cell. The students then took turns to pick a $2 \times 2$ square of four adjacent cells, and to add 1 to each of the numbers in the four cells. After a while, the grid looked like the diagram on the right (some of the numbers in the cells have been rubbed out.) What number should be in the cell with the question mark?

(A) $9$ (B) $16$ (C) $21$ (D) $29$ (E) $34$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.