Domino

By systematically checking all 28 possible dominoes in a standard double-six set, I identified that the domino with four pips on both ends (double-four) is missing from the 27 dominoes shown in the image. All other combinations from 0-0 through 6-6 are present.

After counting all combinations in the standard double-six set of 28 tiles against the 27 tiles present in the image, the [6, 4] domino is missing. All other combinations (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, 5-5, 5-6, 6-6) are visible.

The excluded domino is number 2 and 1

I systematically catalogued all 27 visible dominoes in the image and compared them against the full standard set of 28 dominoes (0-0 through 6-6). After identifying each tile, I found that the double-blank (0-0) domino is not present in the image.

Counting the number of ends showing each value from 0–6, the counts for 2 and 6 are one short of the expected 7 each (all other numbers appear seven times), so the missing domino is [2,6].

By carefully analyzing the image and counting the occurrences of each number on all visible domino ends, the number 3 appears exactly 7 times (whereas all other numbers from 0-6 should appear 8 times in a complete double-six set of 28 dominoes with 56 total ends). Since the excluded domino [a,b] would cause both a and b to appear 7 times each, and given that the number of 6s also appears reduced in the pattern (with dominoes [2,6], [1,6], and [4,6] visible in the image but [3,6] absent), the excluded domino is [3,6]. The dominoes present containing 3 are: [3,4] (twice), [1,3] (twice), [3,3] (double), and [0,3], totaling 7 occurrences of the number 3, confirming that the missing domino contains a 3.