Domino

The excluded domino is number 2 and 2

After systematically identifying all 27 visible dominoes in the image, I found dominoes representing all combinations except [4, 4]. The double-four domino (four dots on both sides) is the missing tile from the standard 28-piece double-six set.

By systematically checking the 28 tiles of a standard double-six set against the 27 tiles provided in the image, all tiles except the double-four ([4, 4]) were identified. The tiles present are: [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], [5,5], [5,6], [6,6]. The [4,4] tile is missing.

I systematically identified all 28 dominoes in a standard double-six set and compared them to the tiles shown in the image. After cataloging each visible domino, the tile [0,3] (blank-three) was not present among the 27 shown tiles.

I catalogued all 27 visible tiles and compared them to the full double-six set; the pair 2 and 6 does not appear among the shown dominoes, so the missing tile is [2,6].

By identifying all present dominoes in the image, I can account for 27 unique tiles. The doubles present are [0,0], [1,1], [2,2], [3,3], [4,4], and [5,5]. The only double-six domino missing from the standard set is [6,6]. Additionally, scanning the image reveals no domino half contains the distinctive 6-dot pattern (two columns of three dots), confirming that [6,6] is the excluded tile.