Domino

The excluded domino is number 3 and 4

After cataloging all 27 dominoes shown in the image, the set contains: [0,0], [2,3], [0,2], [1,2], [2,4], [3,5], [5,5], [0,3], [3,4], [5,6], [0,1], [0,6], [4,4], [0,4], [6,6] is missing, [3,6], [2,6], [2,5], [4,5], [0,5], [1,3], [3,3], [1,5], [1,4], [1,6], [2,2], [1,1]. The double-six tile [6,6] is the only one absent from the standard 28-tile set.

By systematically checking all 28 possible dominoes in a standard double-six set (representing pairs from 0-0 to 6-6), I identified 27 dominoes in the image. The missing domino is [0, 1], which would show a blank (0 dots) on one half and a single dot (1 dot) on the other half. This domino is not present among the visible tiles.

I systematically catalogued all visible dominoes in the image. A standard double-six set has 28 tiles. After identifying all 27 visible tiles, the missing one is [0,3] - a blank/three combination which does not appear anywhere in the image.

I identified and listed the 27 visible tiles and compared them to the full double-six set (all unordered pairs 0–6). Every pair appears except the 3–5 tile, so the excluded domino is [3,5].

After carefully analyzing the arrangement and counting the pips in each half of the 27 dominoes shown in the image, all unique pairs from the standard double-six set are present except for the [2|6] domino. The counts for numbers 2 and 6 are 7 each, while others are 8.