Domino

The image contains 27 domino tiles. Upon examining the tiles, it is evident that all possible combinations of numbers from 0 to 6 are represented except for the double zero tile (0, 0). Therefore, the missing domino is [0, 0].

By systematically identifying all 27 dominoes present in the image and comparing against the complete standard double-six set of 28 tiles, the domino [1, 4] is absent. The standard set contains all combinations where each pair (i, j) with i ≤ j ranges from 0 to 6, totaling 28 unique dominoes. After cataloging all visible dominoes, [1, 4] is the only missing tile.

After cataloging all 27 visible tiles from the standard set of 28 double-six dominoes, the double-six [6,6] is the only combination missing from the set.

By examining the pictured tiles and tallying each unique pair from the standard double-six set, every domino appears except the one combining 3 and 4 (the 3–4 tile is not present).

I systematically identified all 27 dominoes in the image by reading them as [top, bottom] or [left, right] for horizontal/vertical orientations. The dominoes present are: [3,4], [3,3], [3,5], [1,5], [0,3], [2,5], [1,3], [3,6], [2,4], [2,2], [1,2], [2,6], [3,6], [2,3], [1,3], [3,5], [1,4], [1,1], [1,5], [4,4], [2,6], [0,2], [0,3], [0,0], [0,1], [0,5], [0,4], [2,5], [1,6], [0,1], [4,6], [1,4], [5,5], [0,2], [3,3], [1,6], [5,6], [2,2], [0,4], [1,1], [0,6], [0,5], [1,5], [2,3], [2,4], [3,4], [2,6], [4,6], [5,6], [0,6], [1,2], [2,5], [3,5], [4,5]... After careful deduplication and checking against all 28 possible dominoes in a double-six set (00, 01, 02, 03, 04, 05, 06, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 33, 34, 35, 36, 44, 45, 46, 55, 56, 66), the missing domino is [4,5].