Domino

After carefully cataloging all 27 visible dominoes in the image and comparing them against the full 28-tile standard double-six set, the domino [0,3] (blank-three) is the one that does not appear in the image.

By systematically examining all 27 dominoes visible in the image and comparing them to the 28 tiles in a standard double-six domino set, I identified all tiles from [0,0] through [6,6]. The domino [4,4] (double four) is not present in the image, making it the excluded domino from the complete set.

The excluded domino is number 1 and 6

I counted the pips on each half of the 27 shown tiles. Every pip value 0–6 appears eight times in a full double-six set; in the picture all values appear eight times except 2 and 5, which each appear only seven times. Therefore the missing domino must contain 2 and 5 — the excluded domino is [2,5].

By analyzing the dominoes present in the image, I identified 27 tiles. A standard double-six set contains 28 tiles. Counting the occurrences of each number: 0 appears 7 times (in [0,0], [0,1], [0,2], [0,3], [0,5], [0,6]), 1 appears 8 times, 2 appears 8 times, 3 appears 8 times, 4 appears 7 times (in [1,4], [2,4], [3,4], [4,6]), 5 appears 8 times, and 6 appears 8 times. Since numbers 0 and 4 each appear only 7 times instead of 8, the missing domino must be the one containing both 0 and 4, which is [0,4].