Domino

After systematically examining all 27 visible dominoes in the image, I identified each unique tile. A standard double-six domino set contains 28 tiles representing all possible combinations from [0,0] through [6,6]. The domino [4,4] (double-four) is the only tile from the complete set that does not appear in this image, making it the excluded domino.

The image contains 27 dominoes. A standard double-six domino set has 28 tiles. By examining the given dominoes, we can identify that the missing domino is [0, 0] as it is not present in the image.

A full double-six domino set consists of 28 tiles. Upon tallying the tiles present 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, 4-6, 5-5, and 5-6 are all accounted for. The only tile from the standard 28-piece set missing is the double-six (6-6).

I need to find which domino is missing from the standard 28-tile double-six set. Let me identify all the dominoes present by reading their pips. Going through systematically: [0,0], [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], [4,5], [4,6], [5,5], [5,6], [6,6], [0,1], [0,6]. Wait, let me recount more carefully by looking at the image. Row by row: [0,3], [1,3], [2,4], [3,4], [1,2], [2,2], [0,2], [0,1], [2,3], [3,3], [0,0], [1,1], [1,4], [2,5], [3,5], [1,5], [2,6], [4,5], [4,6], [5,6], [5,5], [6,6], [0,6], [1,6], [3,6], [0,4], [0,5]. Checking against all 28 possible pairs from 0-6: [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]. After careful analysis, [4,4] (double-four) is the only domino not present in the image.

After counting the occurrences of each number of pips across all 54 halves in the 27 dominoes, the number 4 appears in 7 halves, the number 6 appears in 7 halves, and all other numbers 0-3 and 5 appear in 8 halves each. This indicates the missing domino from the standard set is the one with 4 and 6.

Counting the pips on each half of the 27 tiles shows the numbers 4 and 6 each occur one time fewer than expected (7 occurrences instead of 8). All other numbers appear 8 times, so the missing tile must be the 4–6 domino.