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IMSO 2024 — Mathematics Exploration Question 3

IMSO Maths · IMSO 2024 — Mathematics Exploration

Question 3

A standard domino set has 28 pieces: 6-6, 6-5, 6-4, 6-3, 6-2, 6-1, 6-0, 5-5, 5-4, 5-3, 5-2, 5-1, 5-0, 4-4, 4-3, 4-2, 4-1, 4-0, 3-3, 3-2, 3-1, 3-0, 2-2, 2-1, 2-0, 1-1, 1-0, 0-0.

a. In the left diagram, a standard set is laid out in an $8\times8$ grid. Mark the domino positions in pencil. The checklist at right may help: cross out each found domino. The 0-0 domino has already been marked.

Question illustration

b. Bold lines show domino positions. Numbers beside each row and below each column must occur in that row or column, not necessarily in the given order. In a horizontal domino, the smaller number is on the right; in a vertical domino it is at the top. Each colored domino has equal numbers. Complete the $8\times8$ grid.

Question illustration

Editorial source note: both figures actually show 7 rows and 8 columns. The original wording and numbers are retained; see the solution for further contradictions.