Domino

The excluded domino is number 2 and 2

By systematically checking all 28 possible dominoes in a standard double-six set, I identified 27 dominoes in the image. The domino with 4 dots on one end and 5 dots on the other (or equivalently [5, 4]) is the only one missing from the complete set of all possible pairings from 0-6.

By systematically going through all 28 dominoes in a standard double-six set and comparing with the image, I can identify each domino present. The full set includes all combinations from [0,0] to [6,6]. After carefully cataloging all visible dominoes in the image, the [0,3] domino (blank-three) appears to be missing.

I identified and tallied the 27 visible tiles from the standard double-six set; every pair from 0–6 appears except the domino with 4 and 6, so the excluded domino is [4,6].

After analyzing the ASCII art, all dominoes from [0,1] to [6,6] are present except the double zero [0,0], as the counts show 0 appears only 6 times, indicating a missing double zero which contributes two 0’s.

The standard double-six domino set contains 28 tiles where each number 0-6 should appear exactly 8 times across all tiles. After carefully counting all 27 visible dominoes in the image, the counts are: 0 appears 8 times, 2 appears 8 times, 3 appears 8 times, 4 appears 7 times (missing one), 5 appears 8 times, 6 appears 8 times, and 1 appears 7 times (missing one). The only standard domino that would account for both digit 1 and digit 4 each missing one occurrence is the [1,4] tile. The dominoes [0,4] and [0,1] are present in the image, confirming that [1,4] is the one missing from the complete set.