Domino

The excluded domino is number 0 and 1

A full double-six set contains 28 tiles. By counting the tiles in the image, I found: blanks ([0,0], [0,1], [0,2], [0,3], [0,4], [0,5]), ones ([1,1], [1,2], [1,3], [1,4], [1,5], [1,6]), twos ([2,2], [2,3], [2,4], [2,5], [2,6]), threes ([3,3], [3,4], [3,5], [3,6]), fours ([4,4], [4,5], [4,6]), fives ([5,5], [5,6]), and sixes ([6,6]). The only tile from the standard set missing is the blank-six [0, 6].

After carefully cataloging all visible dominoes in the image and comparing against the full standard set of 28 dominoes (0-0 through 6-6), the domino [0,3] (blank-3) appears to be missing from the set.

I scanned the 27 visible tiles and tallied occurrences of each face value (0–6). Every number except 4 and 5 appears seven times, while 4 and 5 each appear only six times, so the missing domino is [4,5].

By counting the occurrences of each number across all halves in the 27 dominoes shown, the numbers 3 and 5 each appear 7 times, while all other numbers (0, 1, 2, 4, 6) appear 8 times. This indicates that the missing domino is the one connecting 3 and 5.

By identifying all 27 present dominoes in the image and comparing against the standard 28-domino double-six set, every domino except [0,1] is accounted for. The present dominoes include: [0,0], [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], [6,6]. The only missing tile is [0,1].