Domino

The excluded domino is number 2 and 2

By systematically checking each tile in a double-six set (from [0,0] to [6,6]), I found that all tiles are present except for the one containing 4 and 6 dots.

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete standard double-six set of 28 tiles (which contains all combinations of numbers 0-6), the domino [4, 4] is the only tile that is not present. All other unique combinations from [0, 0] through [6, 6] appear in the image.

By systematically cataloging all visible dominoes in the image and comparing against the full standard set of 28 dominoes (0-0 through 6-6), the domino with values 0 and 3 appears to be missing from the arrangement.

I catalogued each domino shown and compared against the complete double-six set (all pairs 0–6). Every tile appears except the double-six (6,6), so that is the missing domino.

After carefully examining the image and identifying the pip counts on each of the 27 domino halves, all combinations from [0,0] to [6,6] are present except for [4,6]. The frequency of 4 and 6 each appears 7 times, confirming the missing tile.

By systematically identifying all 27 visible dominoes in the image and comparing against the complete set of 28 double-six dominoes, I found that all dominoes are present except the double-six [6,6]. The identified dominoes include: [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], [2,4], [2,5], [2,6], [3,3], [3,4], [3,5], [3,6], [4,4], [4,5], [4,6], [5,5], [5,6]. The only missing tile is [6,6].