Domino

The excluded domino is number 2 and 6

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete standard double-six set (which contains all combinations of numbers 0-6), the domino [2, 4] is the only tile missing from the set. All other 27 tiles representing pairs like [0,0], [0,1] through [6,6] are present in the image.

By systematically going through all 28 possible domino combinations in a standard double-six set (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) and comparing against the 27 dominoes shown in the image, the domino [0,3] (blank-three) is not present in the image.

After identifying all visible tiles, every double from 0–5 appears but there is no double-six tile (no domino showing six pips on both halves), so the missing domino is [6,6].

In a standard double-six domino set, there are 28 dominoes where each number 0-6 appears exactly 7 times across all dominoes. By carefully examining the image and counting the occurrences of each number on the visible dominoes, the numbers 3 and 4 each appear only 6 times instead of the expected 7. All other numbers (0, 1, 2, 5, 6) appear the correct number of times (7 times each). Since the missing domino [3|4] would account for one occurrence of both 3 and 4, this confirms that the [3|4] domino is the one excluded from the set. The puzzle shows 27 dominoes arranged in a pattern, and [3|4] is the only domino from the complete double-six set that is not present.