Domino

Reasoning

The excluded domino is number 2 and 1

Reasoning

A standard double-six domino set consists of 28 tiles. The image shows 27 tiles. Analyzing the provided tiles, we can identify all pairs from 0 to 6 that are present: Pairs with 0: (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6) - All 6 are present. Pairs with 1: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) - All 6 are present. Pairs with 2: (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) - All 5 are present. (The (2, 2) is verified.) Pairs with 3: (3, 3), (3, 4), (3, 5), (3, 6) - All 4 are present. Pairs with 4: (4, 5), (4, 6) - (4, 4) is missing, and (4, 0), (4, 1), (4, 2), (4, 3) are already counted with the other numbers. Pairs with 5: (5, 5), (5, 6) - All 2 are present. Pairs with 6: (6, 6) - Present. Listing the presence of all 28 possible tiles (P = Present, M = Missing): 0-0 P, 1-0 P, 2-0 P, 3-0 P, 4-0 P, 5-0 P, 6-0 P 1-1 P, 2-1 P, 3-1 P, 4-1 P, 5-1 P, 6-1 P 2-2 P, 3-2 P, 4-2 P, 5-2 P, 6-2 P 3-3 P, 4-3 P, 5-3 P, 6-3 P 4-4 M, 5-4 P, 6-4 P 5-5 P, 6-5 P 6-6 P The only domino tile not visible in the image is the [4, 4] (double four).

Reasoning

I inspected the 27 tiles in the image and matched them to the full double-six set; every domino pair from 0–6 appears except the double six [6,6], which is missing.

Reasoning

By counting the occurrences of each number (0-6) on the dominoes, the numbers 3 and 5 each appear one less time than expected in a full double-six set (which requires 8 occurrences per number). This indicates the missing domino is [3,5], as it would account for the missing occurrences of both numbers.

Reasoning

By counting the occurrences of each number across all halves of the 27 dominoes, numbers 0,1,2,5,6 appear 8 times each, while 3 and 4 appear 7 times each. Therefore, the missing domino pairs 3 and 4.

Reasoning

By systematically checking all 28 possible combinations of dominoes in a standard double-six set (all pairs from 0-0 to 6-6), the domino [4, 4] is the only one not present in the image. All other dominoes including [0,0], [1,1], [2,2], [3,3], [5,5], [6,6] and their various combinations are visible.