Domino

The excluded domino is number 2 and 1

After listing all 28 tiles of a standard double-six set and comparing them to the 27 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, 5-5, 5-6), the only tile missing is the double-six (6-6).

By systematically checking all 28 possible dominoes in a standard double-six set, I identified 27 dominoes present in the image. The domino [4, 5] (representing 4 dots on one side and 5 dots on the other) is not present among the visible tiles, making it the excluded domino.

Counting the pips on all 27 tiles shows the face ’6’ appears only 6 times instead of the expected 8 (each number should appear 8 times in a full double-six set). That deficit of two occurrences means the double-six tile (6|6) is missing.

Looking at the image containing 27 dominoes from a standard double-six set (which has 28 dominoes total), I need to identify the missing domino by counting the occurrences of each pip value. In a complete set, each number 0-6 appears exactly 8 times across all domino halves. By examining the dominoes present in the grid: - [0,0], [0,1], [0,3] appear, but [0,2] is nowhere to be found - Counting the zeros: I find [0,0] (2 zeros), [0,1], and [0,3] appears three times, totaling only 7 occurrences - Number 2 appears in [2,3], [2,4], [2,2], and [2,5], but counting carefully shows it would have only 7 occurrences without [0,2] The missing domino is [0,2] because it completes the sequence of dominoes with 0 on one side (having [0,0], [0,1], [0,3] present but not [0,2]), and it accounts for both the missing zero and the missing two needed to reach the required count of 8 appearances for each number.