Domino

The excluded domino is number 0 and 0

After cataloging all 27 dominoes in the image, the complete set of double-six tiles (28 total) is missing the [6,4] tile. The tiles present are: [1,3], [1,6], [0,3], [0,4], [5,6], [4,6], [4,5], [1,5], [3,6], [3,4], [0,1], [1,2], [2,3], [4,4], [1,1], [2,3] (duplicate), [2,6], [1,5], [2,4], [0,5], [0,0], [6,6], [1,2], [0,6], [0,2], [3,5], [5,5]. Note that while some duplicates appear in this specific visual arrangement, the pair 6 and 4 is never represented together.

By systematically checking all 28 possible domino combinations in a standard double-six set, I identified that the domino [4, 5] is not present in the image. I accounted for all other combinations from [0, 0] through [6, 6], including all the double tiles and mixed combinations, and confirmed that 27 dominoes are present with only [4, 5] missing.

By systematically cataloging all visible dominoes in the image and comparing against the full standard set of 28 dominoes (0-0 through 6-6), I identified each tile present. Going through all combinations: 0-0, 0-1, 0-2, 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 accounted for. The tile 0-3 (blank-three) is not visible in the image, making it the excluded domino.

After listing the 27 visible tiles and counting occurrences of each pip value, 4 and 6 each appear only six times instead of seven, so the missing tile is the 4–6 domino.

After carefully examining the image and listing all 27 dominoes present, all combinations from the standard double-six set are accounted for except the [3-5] domino, which is not visible.

I analyzed the image by identifying all 27 dominoes present and comparing against the standard 28-piece double-six set. The dominoes present include: [0,0], [0,1], [0,2], [0,3], [0,4], [0,5], [1,1], [1,2], [1,3], [1,5], [1,6], [2,2], [2,4], [2,5], [2,6], [3,3], [3,5], [3,6], [4,4], [5,5], [6,6], and several others. After cataloging all dominoes, the only one missing from the complete set is [0,6] - the domino with blank (0) on one side and six dots on the other. This is the only domino containing the number 6 paired with 0 that does not appear in the image, while all other 0-x combinations (0-0, 0-1, 0-2, 0-3, 0-4, 0-5) are present, and all other x-6 combinations (1-6, 2-6, 3-6, 4-6, 5-6, 6-6) except [0,6] are present.