Domino

The excluded domino is number 3 and 3

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete standard double-six set of 28 tiles, the domino [0, 1] (one blank side and one pip) is the only tile missing from the set.

I systematically catalogued all 27 visible dominoes in the image and compared them to the full set of 28 dominoes. After identifying each tile, the blank-blank (0-0) domino was not found among the 27 shown.

By cataloging all 27 visible dominoes from the double-six set, I identified 0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 0-6, 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, and 5-6. The only tile from the standard 28-piece set not present is 6-6.

I identified every domino pair from 0–6 except the double-six; there is no tile showing six pips on both ends, so [6,6] is missing.

A standard double-six domino set contains 28 unique dominoes. By systematically examining the 27 dominoes visible in the image, I identified the following 0-suite dominoes: [0,0] (row 3, position 5 - vertical), [0,1] (row 6, position 1 - horizontal), [0,2] (row 5, position 3 - vertical), [0,3] (row 1, position 5 - vertical), [0,4] (row 5, position 2 - horizontal), and [0,5] (row 3, position 1 - vertical). The domino [0,6] is the only member of the 0-suite that is absent from the image, making it the excluded domino. All other dominoes in the set can be accounted for in the various positions throughout the grid.