Domino

The domino [2, 2] is missing from the given set of 27 dominoes.

A standard double-six domino set consists of 28 tiles. Upon tallying the 27 tiles present in the image, the domino with the number pair 1 and 5 is missing.

By systematically identifying all 27 dominoes present in the image and comparing against the complete set of 28 unique dominoes (all pairs from 0-6), the missing domino is [2, 4]. This domino is not visible anywhere in the image while all other 27 combinations are accounted for.

By systematically cataloging all visible dominoes in the image and comparing them to the complete set of 28 dominoes in a standard double-six set, I can identify which one is missing. After counting all the tiles visible, the domino [0,3] (blank-three) appears to be absent from the arrangement.

Every number 0–6 appears the expected number of times except 6, which appears one time fewer than it should (6 instead of 7). No tile shows six on both ends, so the missing tile is the double-six [6,6].

By analyzing the set of 27 visible dominoes and counting the occurrences of each number, I found that the number 0 appears 8 times (in [0,0], [0,1] twice, [0,3] twice, [0,4] twice, and [0,6] once), the number 1 appears 8 times, and other numbers also appear with appropriate frequencies. The only domino from the standard double-six set that is not present in the image is [0,2]. This is confirmed by checking that all other dominoes containing 0 are accounted for: [0,0], [0,1], [0,3], [0,4], [0,5], [0,6] are all visible, leaving [0,2] as the missing tile.