Domino

The excluded domino is number 2 and 2

A double-six domino set contains 28 tiles. By counting the tiles in the image: doubles (0-0, 1-1, 2-2, 3-3, 4-4, 5-5, 6-6) are all present; sequences for 1, 2, 3, 4, and 5 are fully accounted for. When checking the ’blank’ (0) series, we find 0-0, 0-1, 0-2, 0-3, 0-4, and 0-5. The 0-6 tile is missing from the image.

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete standard double-six set of 28 tiles, the domino [4, 5] is the only tile not present. All other combinations of numbers 0-6 appear in the image, making [4, 5] the excluded domino.

After identifying and listing the 27 visible tiles and comparing them to the full double-six set, every domino pair except 4 and 6 appears once, so the missing domino is [4,6].

By carefully cataloging all 27 visible dominoes in the image and comparing them against the full 28-tile standard double-six set, I can identify which tile is missing. The full set includes all combinations from [0,0] to [6,6]. After accounting for all visible tiles, the [0,2] domino (blank-two) is not present in the image.

The excluded domino is number 5 and 3

I identified all 27 dominoes in the image by examining each tile. The complete standard double-six set contains 28 dominoes: [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], [4,4], [4,5], [4,6], [5,5], [5,6], and [6,6]. By checking the dominoes with 0: [0,0] is present (row 4, col 1), [0,1] is present (bottom row, last), [0,2] is present (row 2, col 3), [0,3] is present (row 3, col 2), [0,4] is present (bottom row, col 3), [0,5] is present (row 2, col 2), but [0,6] is not found anywhere in the image. All other dominoes are accounted for, making [0,6] the missing tile.