Domino

The excluded domino is number 3 and 6

I systematically went through all 28 dominoes in a standard double-six set and compared them to the image. After cataloging all visible dominoes, the [0,1] (or [1,0]) domino is missing from the set.

By systematically cataloging all visible dominoes in the image and comparing them to the complete set of 28 tiles in a standard double-six domino set, the domino [0, 1] is the only tile that does not appear among the 27 dominoes shown. All other possible combinations of numbers 0-6 are present in the image.

By visually inspecting the 27 dominoes in the image and comparing to the standard double-six set, all dominoes are present except [2|6]. Alternatively, counting the appearances: numbers 0,1,3,4,5 appear 8 times each, while 2 and 6 appear 7 times each, confirming the missing tile is [2|6].

By identifying all 27 dominoes in the image and cross-referencing with the complete set of 28 double-six dominoes, every domino is accounted for except [1,1]. The complete list of present dominoes includes: [0,0], [0,1], [0,2], [0,3], [0,4], [0,5], [0,6], [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 [1,1].