Domino

A standard double-six domino set contains 28 tiles. Upon listing all the tiles present in the image (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, 5-6, 6-6), the only tile missing from the set is the double-five [5, 5].

By systematically checking all 28 possible domino combinations in a standard double-six set (dominoes with pips from 0-6), I identified that the domino [4, 5] is not present in the image. All other 27 dominoes (including [0,0] through [6,6]) are visible in the collection shown.

The excluded domino is number 2 and 2

By systematically cataloging all visible dominoes in the image and comparing them to the full standard set of 28 dominoes (0-0 through 6-6), the domino [0,3] appears to be missing from the set.

Counting the pips on each visible tile shows the face 6 appears one fewer time than the required seven occurrences, indicating the missing tile is the double-six (6,6).

By carefully analyzing the ASCII art representation of the 27 dominoes and identifying the pip counts in each half of every tile, all combinations from the standard double-six set are present except for the [3|5] domino.

By analyzing the frequency of each number (0-6) appearing across all domino halves in the puzzle, the number 0 appears exactly 7 times and the number 4 appears exactly 7 times. In a standard double-six domino set, each number should appear exactly 8 times. The only domino that involves both the number 0 and the number 4 is [0,4]. Since both counts are deficient by exactly 1, the excluded domino must be [0,4].