Domino

After cataloging all 27 visible tiles, it is determined that all tiles from the standard double-six set are present except for the double-six (6-6) tile.

The excluded domino is number 2 and 2

By systematically checking all 28 possible domino combinations (each pair of numbers from 0-6, including doubles), I identified that the domino [2, 4] is the only one missing from the 27 dominoes shown in the image. All other combinations including [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], [2,5], [2,6], [3,3], [3,4], [3,5], [3,6], [4,4], [4,5], [4,6], [5,5], [5,6], and [6,6] are present in the image.

By systematically cataloging all visible dominoes in the image and comparing them to the complete set of 28 dominoes in a standard double-six set, I can identify which one is missing. After carefully examining each domino in the image and listing all pairs present, the domino [0,3] (blank-three) is not found among the 27 displayed dominoes.

I tallied the pips on each half of the 27 visible tiles. Every number 0–6 appears the expected number of times except 2 and 5, which each appear one time fewer than they should in a complete double-six set. Therefore the missing tile is the 2–5 domino.

After systematically identifying all 27 visible dominoes in the image, I accounted for the presence of [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5], as well as all other dominoes involving numbers 1-5. The only domino not present in the image is [0,6], which would complete the standard double-six set. Specifically, the domino with 0 dots on one half and 6 dots (arranged as two columns of three) on the other half is missing.