Domino

The excluded domino is number 2 and 1

After listing and checking all 27 dominoes shown in the image against the standard set of 28 double-six dominoes, the double-six tile (6, 6) is the only one not present.

By systematically checking all 28 possible dominoes (0-0 through 6-6), I identified that the domino [2, 5] is the only one missing from the set. All other 27 dominoes from a standard double-six set are present in the image.

I systematically went through all 28 dominoes in a standard double-six set and checked each one against the image. After carefully counting all visible dominoes and mapping them to their values, the domino [0,2] (blank-two) appears to be missing from the set.

Counting the pips on the 27 visible tiles shows the 4 and the 6 each appear one time fewer than they should in a complete double-six set (each number should appear 7 times). The only tile that would add one 4 and one 6 is the 4–6 domino, so that domino is missing.

By analyzing the image and counting the occurrences of each number on the domino halves, numbers 0, 1, 2, 4, and 6 appear 8 times each, while 3 and 5 appear 7 times each, indicating the missing domino is [3|5].

By analyzing the frequency of each number on all visible domino ends, the number 5 appears 7 times and the number 6 appears 7 times, indicating the missing domino contains both 5 and 6. All other number combinations are accounted for in the 27 visible dominoes.