Domino

A standard double-six domino set consists of 28 tiles. Upon tallying the tiles shown in the image, there are 27 present. By checking each combination of numbers from 0-0 to 6-6, it is determined that the [1, 6] tile is the only one missing from the collection.

The excluded domino is number 0 and 0

By systematically cataloging all visible dominoes in the image and comparing them against the complete standard set of 28 dominoes (all pairs from 0-0 to 6-6), I can identify which tile is missing. After going through each domino visible in the image, the [0,6] domino (blank/six) is not present among the 27 shown tiles.

By systematically cataloging all 27 visible dominoes in the image across each row and comparing them to the complete set of 28 possible dominoes (all combinations of numbers 0-6), the domino [2, 4] is the only one not present. All other combinations including [0,0], [0,1] through [0,6], [1,1] through [1,6], [2,2], [2,3], [2,5], [2,6], [3,3] through [3,6], [4,4] through [4,6], [5,5], [5,6], and [6,6] are accounted for in the image.

After identifying the 27 visible tiles and checking all combinations 0–6, the only missing pair is 1 and 4, so the excluded domino is [1,4]

Scanning the complete set of visible dominoes, I identified all dominoes containing 0: [0,0], [0,1], [0,2], [0,3], [0,4], and [0,6]. The domino [0,6] appears in row 2, position 5 (vertical orientation with blank top and 2x3 dot pattern on bottom). The domino [0,5] with five dots (four corners plus center) is not present in any of the 27 tiles. A complete double-six set must contain seven dominoes with 0, and only six are visible, with [0,5] being the only one not found.