Domino

The excluded domino is number 2 and 1

By systematically checking all 28 possible domino combinations in a standard double-six set (all pairs from 0-0 to 6-6), the domino [2, 4] is not visible in the image. All other 27 dominoes are present, including [0, 0], [0, 1] through [0, 6], [1, 1] through [1, 6], [2, 2], [2, 3], [2, 5], [2, 6], and all remaining combinations up to [6, 6].

After cataloging all 27 tiles present in the image, all combinations from the standard double-six set (0-0 through 6-6) are found except for the double-six (6-6) tile.

I identified and listed the 27 visible tiles and compared them to the full double-six set. All tiles from (0,0) to (6,6) appear except the 4–6 tile, so the excluded domino is [4,6].

The full set of 28 double-six dominoes contains: [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], [5,6], [6,6]. After identifying 27 dominoes in the image, the following are present: [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], [5,5], [5,6], [6,6]. The only domino from the complete set not found in the image is [4,6]. Specifically, [4,5] appears in row 4, column 4 (vertical), [5,6] appears in row 5, column 6 (vertical with 5 dots on top and 6 on bottom), and [4,6] is nowhere to be found.