Domino

After cataloging all 27 visible dominoes in the image, the missing tile from the standard double-six set (28 tiles) is identified as the double-five ([5, 5]) tile.

The excluded domino is number 2 and 2

After systematically cataloging all 27 visible dominoes in the image and checking against the standard 28-tile double-six set (which contains all unique combinations where each number from 0-6 pairs with every number from 0-6 with equal or higher value), the domino [1, 4] is the only tile not present in the collection.

After carefully cataloging all 27 visible dominoes in the image and comparing them to the full standard set of 28 dominoes (all pairs from 0-0 to 6-6), I found that the double-one tile [1,1] is missing from the set.

Counting the pips on the 27 tiles shows every face value 0–5 appears 8 times across all ends, while the face 6 appears only 6 times, indicating the double-six (6,6) is missing.

Upon analyzing the grid of dominoes, the domino [3,3] (showing three dots on both ends) appears twice in the puzzle - once in row 4 and once in row 5. In a standard domino puzzle where each domino value should appear exactly once, the duplicate [3,3] is the excluded/extra domino that breaks the pattern of uniqueness. While other dominoes like [1,5] and [0,3] may also appear to be duplicated upon close inspection, the [3,3] domino is the clearest and most certain duplicate based on the visible dot patterns, making it the excluded domino in this puzzle.