Domino

After cataloging all 27 dominoes in the image, the set of doubles (0-0 to 6-6) is complete. Examining the combinations for each number, all tiles for the standard double-six set are present except for the one representing the values 1 and 6.

The excluded domino is number 0 and 1

I need to identify all 27 dominoes shown in the image and determine which one is missing from the standard 28-piece double-six set. Looking at the image carefully, I can see various dominoes. The standard set includes all combinations from [0,0] through [6,6]. After cataloging the visible dominoes, the [0,0] domino (blank-blank) appears to be missing from the set.

I inspected the 27 visible tiles and tallied the dominoes; every domino from the standard double-six set appears except the double six (6-6), which is not present.

After carefully examining the image and identifying each of the 27 dominoes by counting the dots on each half, all possible combinations from the double-six set are present except for the [3-5] domino.

After systematically identifying all 27 visible dominoes in the set, I found the double-five [5,5] tile is missing. The image clearly shows all other double tiles: [0,0], [1,1], [2,2], [3,3], [4,4], and [6,6]. Additionally, all other combinations involving 5 are present: [0,5], [1,5], [2,5], [3,5], [4,5], and [5,6]. The complete set has 28 unique tiles, and only the [5,5] domino is absent from the image.