Domino

The excluded domino is number 3 and 3

By systematically checking all 28 tiles of a standard double-six set against the 27 tiles provided in the image, it is determined that the [1, 1] tile (double-one) is the only one missing.

By systematically cataloging all 27 visible dominoes in the image, I identified every unique domino present. Comparing against the complete standard double-six set of 28 dominoes (all combinations of 0-6), the domino [4, 4] is the only one missing. This is the double-four tile, which should appear in the full set but is absent from the image.

I systematically catalogued all visible dominoes in the image and compared them against the complete set of 28 dominoes (0-0 through 6-6). After identifying each tile: [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],[5,6],[6,6] are all present. The double-blank [0,0] domino is missing from the image.

I counted the occurrences of each face value on the 27 tiles. Every number 0–6 should appear 8 times in a full double-six set; the value 6 appears only 6 times in the image (two fewer than expected), so the missing domino is the double six [6,6].

By counting the occurrences of each number across all halves of the 27 dominoes shown, each number from 0 to 6 should appear 8 times in a complete set. Numbers 0, 1, 4, 5, and 6 appear 8 times each, while 2 and 3 appear 7 times each, indicating the missing domino is [2, 3].

By systematically identifying all 27 dominoes in the image and comparing against the standard 28 domino set (double-six), the present dominoes are: [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], [5,6], and [6,6]. The only missing tile from the complete set is [5,5].