Domino

The excluded domino is number 3 and 3

After cataloging all 27 tiles present in the image against a standard double-six set, the 6-6 tile is the only one missing.

By systematically counting all dominoes visible in the image across all positions and comparing against the 28 tiles in a standard double-six domino set (which includes all combinations from [0,0] to [6,6]), the domino [4,4] is the only one not present in the image. All other 27 tiles can be identified among the displayed dominoes.

temp

After identifying all visible tiles and checking each unordered pair from 0–6, every domino except the double-six (6,6) appears in the image; the (6,6) tile is not present.

By analyzing the 27 visible dominoes and counting the occurrences of each number (0-6), I find that the number 0 appears 6 times instead of 7, and the number 5 appears 6 times instead of 7. Since each number should appear exactly 7 times in a complete double-six set, the missing domino must be the one that contains both 0 and 5. All other dominoes can be accounted for in the image, including [0,0], [0,2], [0,3], [0,4], [0,6] for the 0s, and [1,5], [3,5], [5,5], [5,6] for the 5s. The only domino that satisfies both missing occurrences is [0,5].