Domino

The excluded domino is number 3 and 3

By systematically checking all 28 possible dominoes in a standard double-six set (all combinations of 0-6 where the first number is less than or equal to the second), the domino [2, 2] is not present in the image. All other dominoes including [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], [3, 3], [2, 3], [2, 4], [2, 5], [2, 6], [3, 4], [3, 5], [3, 6], [4, 4], [4, 5], [4, 6], [5, 5], [5, 6], and [6, 6] are visible in the image.

A standard double-six domino set consists of 28 tiles. By cataloging all 27 tiles present in the image: [1,3], [0,5], [3,6], [5,6], [1,6], [6,6], [2,2], [0,3], [1,2], [1,1], [0,4], [4,6], [1,4], [0,0], [2,6], [1,5], [2,4], [5,5], [4,5], [4,4], [2,5], [0,1], [0,3] (duplicate check), [0,2]-no, [3,4], [1,2] (duplicate check)... After carefully checking the set [0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 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, 6-6], the tile [0,6] is the only one missing.

After carefully examining each domino in the image and cataloging all 27 tiles, I systematically checked which combination from the standard set of 28 dominoes (0-0 through 6-6) is missing. Going through all pairs: 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, 6-6. The domino [1,3] (one pip on one half, three pips on the other) does not appear in the image.

By counting how many times each face value appears among the 27 shown tiles, faces 2 and 5 each appear only six times instead of seven; therefore the missing domino is [2,5].

By counting the occurrences of each number (based on the number of pips in each half) across all 54 halves in the image, each number from 0 to 6 appears 8 times in a complete set. Here, numbers 0, 1, 2, 3, and 6 appear 8 times each, while 4 and 5 appear 7 times each, indicating the missing domino is the one connecting 4 and 5.

By analyzing the 27 dominoes in the image and counting occurrences of each number (0-6), I found that number 0 appears 8 times, number 1 appears 8 times, number 2 appears 7 times, number 3 appears 7 times, number 4 appears 8 times, number 5 appears 7 times, and number 6 appears 7 times. Since each number should appear 8 times in a complete set (or 7 times if it’s on the missing domino), the missing domino must contain the numbers that appear only 7 times: 2 and 6. Therefore, the excluded domino is [2,6].