Domino

The excluded domino is number 2 and 1

By systematically identifying all 27 visible dominoes in the image and comparing them against the complete set of 28 dominoes in a standard double-six set, the domino [4, 4] is the only one not present. All other double tiles [0,0], [1,1], [2,2], [3,3], [5,5], [6,6] and all combination tiles are accounted for.

By systematically checking all 28 tiles of a standard double-six set against the 27 tiles 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, 5-5, 5-6, and 6-6 are all present. The tile containing a 4 and a 6 is missing.

Counting pips on the 27 shown tiles yields two fewer 6-pips than a full double-six set requires (a complete set has fourteen 6-pips), so the missing tile must be the double-six [6,6].

In a standard double-six set, each number (0-6) appears 8 times across all dominoes. Counting the occurrences in the image shows that numbers 2 and 5 each appear 7 times (one less than expected), indicating the missing domino is [2, 5].

By counting the occurrences of each number across all halves of the 27 dominoes, the number 2 appears 7 times and the number 5 appears 7 times, while all other numbers appear 8 times. Therefore, the missing domino is [2|5].

After systematically identifying all 27 dominoes in the image, the complete set includes all dominoes from [0,0] through [5,5] (the double-five set of 21 dominoes) plus six dominoes involving the number 6: [0,6], [1,6], [2,6], [3,6], [4,6], and [5,6]. The only domino from the standard double-six set that is not present is the double-six itself [6,6]. The dominoes involving 6 can be identified in the image: [0,6] and [1,6] appear as vertical dominoes in row 5, [2,6] appears as a vertical domino in row 2, [3,6] appears as the domino [3,5/6] in the top row, [4,6] appears as the rightmost horizontal domino in row 4, and [5,6] appears as [5,5/6] in row 5. The [6,6] domino, which would show 6 dots on both halves, is absent from the collection.