Domino

The excluded domino is number 0 and 0

By systematically checking all 28 possible dominoes in a standard double-six set, I identified that the domino [0,1] (or equivalently [1,0]) is the only one missing from the 27 dominoes shown in the image. All other combinations from [0,0] through [6,6] are present.

A standard double-six set contains 28 tiles. By cataloging the tiles in the image, all tiles from the blanks (0-0 to 0-6), ones (1-1 to 1-6), twos (2-2 to 2-6), threes (3-3 to 3-6), fours (4-4 to 4-6), and fives (5-5 to 5-6) are present, but the double-six [6, 6] tile is missing.

By systematically going through all 28 possible domino combinations in a standard double-six set (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) and comparing against the 27 dominoes visible in the image, the domino [0, 2] (blank-two) appears to be missing.

All other domino combinations from 0–6 appear in the image; the only double missing is 6–6.

Numbers 3 and 5 each appear 7 times across all halves, while all other numbers 0,1,2,4,6 appear 8 times. Thus, the missing domino pairs 3 and 5.

I examined all dominoes in the image and identified 27 unique tiles from the standard double-six set. I can clearly see all dominoes in the ’0’ series: [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5] are all present in the image (both vertical and horizontal orientations). However, the [0,6] domino (blank on one side, six dots on the other) is not visible among the 27 tiles. Since a standard double-six set contains exactly 28 dominoes, and all others are accounted for, the missing tile is [0,6].