Domino

The excluded domino is number 0 and 0

By systematically checking all 28 possible dominoes in a standard double-six set (all pairs from 0-0 to 6-6), I identified 27 dominoes in the image. The double-four (4-4) domino, which should show four dots on both sides, is not present among the visible tiles. This is the missing domino from the complete set.

By cataloging all 27 dominoes present in the image and comparing them against a standard double-six set, which includes all unique combinations from [0,0] to [6,6], it is found that the double-six ([6,6]) tile is the only one not shown.

I systematically counted all dominoes in the image and compared them against the complete set of 28 double-six dominoes (00, 01, 02, 03, 04, 05, 06, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 33, 34, 35, 36, 44, 45, 46, 55, 56, 66). I found all dominoes except [5, 5] (double-five). The counts of each number on the dominoes confirm this: 0 appears 8 times, 1 appears 8 times, 2 appears 8 times, 3 appears 8 times, 4 appears 6 times, 5 appears 4 times (should appear 6 times in a complete set), and 6 appears 8 times. The missing double-five would add two more 5s, bringing the total to 6, matching the expected frequency.

I examined the 27 dominoes in the image and matched them against the full double-six set (all unordered pairs 0–6). Every tile except the double-six (6,6) is present, so the missing tile is the double-six.