Domino

The excluded domino is number 3 and 3

A standard double-six domino set consists of 28 tiles. Upon tallying the tiles in the image, all doubles are present except for the [6, 6] tile. Specifically: [0,0], [1,1], [2,2], [3,3], [4,4], and [5,5] are visible, but the double-six is missing.

By systematically cataloging all visible dominoes in the image and comparing them to a complete set of 28 dominoes (0-0 through 6-6), the domino [0,3] is the one not present in the image.

By systematically checking all 28 possible dominoes in a standard double-six set (all pairs of numbers 0-6), 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.

I checked the image against the full double-six set (all pairs 0–6). Every tile except the double six (6-6) appears in the picture, so the missing domino is [6,6].

By enumerating all 27 dominoes in the image and comparing to the complete set, or equivalently by counting the occurrences of each number across all halves, numbers 2 and 5 appear only 7 times each, while all others appear 8 times.

A standard double-six domino set contains 28 unique tiles. By systematically identifying all dominoes in the image, I can account for 27 of them. The complete set includes all pairs from [0,0] to [6,6]. Looking at the 0-series: [0,0], [0,1], [0,2], [0,3], [0,4], and [0,6] are all clearly visible in the image. The only 0-series domino missing is [0,5], which should have a blank side and a side with 5 pips (four corners plus a center dot). Checking all other dominoes confirms that [0,5] is the one tile not present in the set.