Domino

After listing every unique domino in a standard double-six set (28 tiles total) and comparing it against the 27 tiles present in the image, the only tile not accounted for is the 5-0 (or 0-5) tile.

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete standard double-six set of 28 unique tiles, the double-four (4-4) domino is missing. This domino is not visible anywhere in the grid layout shown.

The excluded domino is number 0 and 0

After systematically 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), the domino [1,3] (one pip on one side, three pips on the other) is the one that does not appear in the image.

I counted the pips on all visible domino halves. Every number 0–6 appears eight times across the set except for 6, which appears only six times on single halves (missing two pips), indicating the double-six tile (6,6) is absent.

By counting the occurrences of each number across all halves of the 27 dominoes in the image, numbers 3 and 5 each appear 7 times, while all other numbers appear 8 times, indicating the missing domino is [3-5].

I analyzed all 27 dominoes in the image to find which one is missing from the standard double-six set. The dominoes present are: [0,1], [0,2], [0,3], [0,4], [0,5]×2, [0,6], [1,2], [1,3]×2, [1,4], [1,6], [2,2], [2,3]×2, [2,4], [2,5], [2,6], [3,3]×2, [3,4], [3,5], [3,6]×2, [4,4], [4,5], [4,6], [5,5], [6,6]. After checking all combinations from 0-6, I found that [1,1] (the double-one domino) is the only tile missing from the complete set.