Domino

By systematically cataloging all 27 visible dominoes in the image and comparing them against the complete standard double-six set of 28 dominoes, the double-four (4,4) domino is the only one missing. All other dominoes from (0,0) through (6,6) are present in the image.

The excluded domino is number 0 and 0

By cataloging all 27 dominoes in the image, I found the following pairs: [1,1], [6,6], [1,6], [2,4], [0,4], [4,5], [0,1], [2,3], [4,6], [0,0], [2,5], [1,4], [3,3], [1,5], [0,5], [0,2], [0,6], [4,4], [2,6], [3,6], [5,5], [1,3], [5,6], [0,3], [3,4], [1,2], and [3,5]. Note that [4,5] appears twice in the visual listing (top-middle-left and bottom-right), while the domino [4,5] is present, cross-referencing the full double-six set reveals that the only unique pair not represented in the set of 27 tiles is [4,5]. However, upon re-examination of the provided image, the tile [4,5] is present, and the tile [4,2] is present. Comparing the list against the 28 standard tiles, the missing tile is [4, 5] if counted as a duplicate or specific omission. Let’s re-verify: the tile [4,5] is present at the bottom right. The tile [5,4] is also in the second row. Checking for [0,4], [1,4], [2,4], [3,4], [4,4], [5,4], [6,4]... all are present. Checking [0,5], [1,5], [2,5], [3,5], [4,5], [5,5], [6,5]... all are present. Re-checking [0,2], [1,2], [2,2], [3,2], [4,2], [5,2], [6,2]... the tile [2,2] is missing from the image.

I identified and listed the 27 visible tiles and compared them to the full double-six set (all pairs 0–6). Every domino from the complete set appears in the image except the double six (6,6), so the missing tile is [6,6].

By analyzing the 27 dominoes present in the image and counting the occurrences of each number (0-6), I determined that the number 4 appears 6 times and the number 5 appears 6 times, while all other numbers appear 7 times each. In a standard double-six set, each number appears exactly 7 times across the 28 dominoes. When one domino is missing, the two numbers on that missing domino will each appear only 6 times. The domino containing both 4 and 5 is [4,5], which is the only one absent from the set.