Domino

By systematically going through all 28 possible domino combinations in a standard double-six set and comparing them to the 27 dominoes visible in the image, I can identify that the [0,3] domino (blank-three) is missing. All other combinations from [0,0] through [6,6] are accounted for in the image.

The excluded domino is number 0 and 0

By systematically checking all 28 possible dominoes in a standard double-six set (every combination of numbers 0-6), I can identify that the domino with 2 dots on one end and 4 dots on the other is not visible in the image. All other 27 dominoes are present.

By systematically checking each tile in a standard double-six domino set (28 tiles total), I identified all existing tiles in the image: [2,2], [1,2], [2,4], [2,3], [0,0], [1,6], [3,4], [6,6], [1,3], [4,4], [0,6], [5,5], [2,6], [0,4], [1,5], [0,5], [5,6], [4,5], [4,6], [2,5], [1,4], [2,5], [0,3], [3,3], [1,1], [0,1], [3,6]. The only missing unique tile is [0,6] or [6,0].

I systematically checked all 28 possible domino combinations in a double-six set (0-0 through 6-6). I found all dominoes present except for the double-six [6,6]. I verified this by checking: all doubles (0-0, 1-1, 2-2, 3-3, 4-4, 5-5 are present, but 6-6 is missing), and all combinations with 6 (0-6, 1-6, 2-6, 3-6, 4-6, 5-6 are present, but 6-6 is missing). The double-six domino would show six dots on both halves.

All other domino pairs from the double-six set appear in the image but the double-six tile (6-6) is not present.

After counting the occurrences of each number across all halves of the 27 dominoes, the numbers 0,1,2,4,5 appear 8 times each, while 3 and 6 appear 7 times each. Thus, the missing domino is [3|6].