Domino

The image contains 27 dominoes, and upon inspection, it is evident that all possible pairs from 0 to 6 are represented except for the double zero (0, 0).

By systematically checking all 28 possible dominoes in a standard double-six set (pairs of numbers from 0 to 6), I identified 27 dominoes in the image. The domino with 0 dots on one side and 1 dot on the other side (the [0,1] domino) is the only one missing from the complete set.

After cataloging all 27 dominoes shown in the image, the set represents a double-six set (28 tiles total). The visible tiles include pairs for all combinations except for the double-six (6, 6). All other doubles [0,0], [1,1], [2,2], [3,3], [4,4], and [5,5] are present.

By systematically cataloging all visible dominoes in the image and comparing against a complete standard double-six set (28 tiles), I identified all present dominoes. The complete set includes every combination from [0,0] to [6,6]. After mapping out all 27 visible tiles, the missing tile is [0,3] (also written as [3,0]).

Every other tile of the double-six set appears in the image; the only double missing is the 6-6 tile.

By analyzing the 27 visible dominoes and counting the occurrences of each number (0-6), I found that the number 0 appears 7 times and the number 5 appears 7 times, while all other numbers appear 8 times. In a complete double-six set, each number appears exactly 8 times across the 28 dominoes. The missing domino must be the one containing both numbers that appear only 7 times. Visible dominoes with 0 include: [0,0], [0,1], [0,2], [0,3], [0,4], and [0,6]. Visible dominoes with 5 include: [1,5], [2,5], [3,5], [4,5], [5,5], and [5,6]. The only combination not present is [0,5].