Domino

The excluded domino is number 3 and 3

After cataloging all 27 dominoes shown in the image and comparing them to a full double-six set of 28 tiles, the [1, 4] (one-four) domino is the only one missing.

By systematically cataloging all 27 visible dominoes in the image and comparing them to the complete standard double-six set of 28 tiles, the domino [4, 4] is missing. The standard set includes one double of each number (0-0, 1-1, 2-2, 3-3, 4-4, 5-5, 6-6) and all unique pairs. All other dominoes are present in the image, making [4, 4] the excluded domino.

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Counting the pips on each half of the 27 shown tiles, the pip ’6’ appears only 6 times while every other pip (0–5) appears 8 times as expected for a full double-six set; therefore two ’6’ pips are missing, so the missing tile is the double six [6,6].

A standard double-six domino set contains 28 tiles. By examining the image, all domino combinations involving 0 are present except [0,6]: [0,0] (third row, center), [0,1] (top row, right), [0,2] (top row), [0,3] (bottom row, horizontal), [0,4] (fourth row, vertical), and [0,5] (fifth row, right side, vertical). The [0,6] domino is the only one missing from the set.