Domino

The excluded domino is number 2 and 2

A standard double-six set contains 28 tiles. By checking the image, we find representatives for all tiles except the double-six [6, 6]. The image contains: [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], [4,6], [5,5], and [5,6]. The [6,6] is missing.

By systematically checking all 28 possible dominoes in a standard double-six set (all pairs of numbers 0-6 including duplicates), I identified 27 dominoes in the image. The domino [2, 4] is the only one missing from the complete set. All other combinations including [0,0], [0,1] through [0,6], [1,1] through [1,6], [2,2], [2,3], [2,5], [2,6], [3,3] through [3,6], [4,4] through [4,6], [5,5], [5,6], and [6,6] are present.

By systematically cataloging all visible dominoes in the image and comparing against the complete set of 28 dominoes (all combinations from 0-0 to 6-6), the domino with values 1 and 3 appears to be missing from the set.

After identifying and tallying each visible tile (all unordered pairs 0–6) every possible combination appears except the double six tile [6,6], so the excluded domino is 6 and 6.

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

I systematically identified all dominoes in the image containing the number 0. The dominoes [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5] are all present. The complete double-six set requires seven dominoes containing 0 (one for each pairing with 0-6). Since only six dominoes with 0 are visible, and [0,6] is nowhere to be found in the image, the missing domino must be [0,6].