Domino

The excluded domino is number 0 and 0

After systematically checking all visible dominoes in the image against the standard 28-tile double-six set, the domino [0,1] (or equivalently [1,0]) is not present. All other combinations of numbers 0-6 appear to be represented in the visible tiles.

After cataloging all visible dominoes in the image, I identified each tile’s pip values. A standard double-six set has 28 tiles. Going through all pairs systematically (0-0, 0-1, 0-2, ... 6-6), I found that the double-one tile [1,1] is not present among the 27 shown dominoes.

Counting the pips on all visible domino ends shows every digit 0–6 appears the full 8 times except for 3 and 5, which appear only 7 times each. The missing tile must pair those two values, so the excluded domino is [5,3].

By analyzing the 27 dominoes present in the image and comparing them against the standard 28-tile double-six set, every domino from [0,0] through [5,6] is accounted for except the double-six [6,6]. The set includes all doubles [0,0], [1,1], [2,2], [3,3], [4,4], and [5,5], as well as all other combinations involving the number 6 ([0,6], [1,6], [2,6], [3,6], [4,6], [5,6]) except for the [6,6] tile itself. The highest-value domino [6,6] (with 12 total dots) is the only one missing from the complete set.