Domino

The excluded domino is number 2 and 2

By systematically cataloging all 27 visible dominoes in the image and checking against the complete standard double-six set of 28 tiles, the domino [0, 1] (one blank side and one side with a single dot) is the only tile not present in the image.

After counting the frequency of each number and identifying the specific tiles present, it was found that the standard double-six set (28 tiles) was missing the [6, 0] or [0, 6] tile (Blank-Six). All other combinations from 0-0 to 6-6 are represented in the provided image.

Counting the pips on each visible domino, every number 0–6 appears on 7 tiles except the 6s, which appear only 6 times. Therefore the missing domino is the double six [6,6].

I systematically counted all 27 dominoes present in the image. The standard double-six set contains 28 unique tiles: [0,0], [0,1], [0,2], [0,3], [0,4], [0,5], [0,6], [1,1], [1,2], [1,3], [1,4], [1,5], [1,6], [2,2], [2,3], [2,4], [2,5], [2,6], [3,3], [3,4], [3,5], [3,6], [4,4], [4,5], [4,6], [5,5], [5,6], [6,6]. By carefully examining each domino in the image and tracking which ones appear, I found that [1,1] (the double-one tile with two pips on both halves) is the only domino missing from the complete set.