Domino

The excluded domino is number 2 and 6

A full double-six domino set contains 28 tiles. Upon counting the tiles present in the image for each number pair: (0,0), (0,1), (0,2), (0,3), (0,4), (0,5), (0,6), (1,1), (1,2), (1,3), (1,4), (1,5), (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), (5,6), and (6,6) were all found. The only missing tile from the complete set is (6,1).

I systematically cataloged all 27 dominoes visible in the image and compared them against the 28 tiles in a standard double-six set. After identifying each domino’s pip counts, the tile with 0 on one side and 3 on the other (0-3) was not found among the 27 shown dominoes.

After identifying and tallying the visible tiles, every tile from the double-six set is present 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 in the 27 dominoes, numbers 0, 1, 2, 4, and 6 appear 8 times each, while 3 and 5 appear 7 times each, indicating that the missing domino is [3|5].

By systematically identifying all 27 visible dominoes and counting the occurrences of each number (0-6), the missing domino can be determined. In a full double-six set, each number appears exactly 8 times across all dominoes. Counting the visible dominoes reveals that the number 4 appears 7 times and the number 5 appears 7 times, while all other numbers appear 8 times (accounting for the exclusion). This indicates the missing domino is [4, 5]. The visible dominoes include duplicates of [0,2], [0,4], and [3,4], along with all doubles except [5,5] and [6,6], [0,0] being present, with [4,5] being the only one from the complete set of 28 that is absent.