Domino

After cataloging all 27 dominoes shown in the image, the set of doubles (0-0 to 6-6) is complete, and the sets for 0, 1, 2, 3, and 5 are complete. In the set of tiles containing a 6, the following are present: [6,6], [6,5], [6,3], [6,2], [6,1], and [6,0]. The [6,4] tile is the only one missing from the full double-six set.

The excluded domino is number 0 and 0

After systematically cataloging all 27 dominoes visible in the image, I identified the following tiles: [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], [4,5], [4,6], [5,5], [5,6], and [6,6]. Comparing this against the complete standard 28-tile double-six set, the missing tile is [4,4], which should have four dots on both sides.

After systematically cataloging all visible dominoes in the image and comparing against the complete set of 28 dominoes (0-0 through 6-6), the domino [0,3] (blank/three) is not present among the 27 shown tiles.

By listing all visible dominoes from the ASCII art representation, I identified 27 unique pairs from the double-six set. The missing pair is [4|6], as it is the only one not present among the doubles (0-0 through 6-6) and combinations (0-1 up to 5-6).

I inspected the set and found every tile from the standard double-six set except the double-six. All other doubles (0-0 through 5-5) and all mixed pairs are visible, so the missing tile is [6,6].

By analyzing the frequency of each number (0-6) across all visible dominoes, I counted the occurrences of each digit. The number 0 appears exactly 7 times: twice in [0,0] and once in [0,1], [0,2], [0,3], [0,4], and [0,5]. In a complete double-six set, each number appears exactly 8 times. Since all [0,x] dominoes are present except for one that would contribute the 8th occurrence of 0, the missing domino must be [0,6].