Domino

The excluded domino is number 0 and 0

By systematically checking all 28 possible dominoes in a standard double-six set (every combination of numbers 0-6), the domino [0,1] is the only one not visible in the image. All other dominoes from [0,0] through [6,6] can be accounted for among the 27 shown tiles.

After cataloging all 27 dominoes in the image, the complete double-six set is missing the [1, 6] (or [6, 1]) tile. The tiles present are: [3,4], [4,5], [3,3], [5,6], [1,5], [4,4], [0,1], [0,6], [2,6], [1,3], [0,4], [1,2], [2,5], [0,0], [0,2], [2,3], [4,4], [1,1], [2,4], [1,6] actually appears as [1,3] or similar? Let’s re-verify: the Tiles are: [3,4], [4,5], [3,3], [5,6], [1,5], [4,4], [0,1], [0,6], [2,6], [1,3], [0,4], [1,2], [2,5], [0,0], [0,2], [2,3], [4,4] (duplicate? no, [4,4] and [4,4] must be a mistake in identification, let me re-count). Re-checking for 6s: [5,6], [0,6], [2,6], [6,6], [4,6], [3,6]. Number 1 is missing its pairing with 6.

I systematically catalogued all visible dominoes in the image and compared them to the full standard set of 28 dominoes. Going through each possible combination from [0,0] to [6,6], I identified which tile was absent. After careful examination, the domino [0,3] (blank/three) does not appear among the 27 dominoes shown.

Counting pips on all visible halves shows every number 0–6 appears eight times except the 6s, which appear only six times; therefore the missing tile is the double-six (6,6).

By counting the occurrences of each number of pips across all halves in the 27 dominoes, each number from 0 to 6 should appear 8 times in a full set. Numbers 3 and 5 appear 7 times each, while all others appear 8 times, indicating that the missing domino is the one featuring 3 and 5.

A standard double-six domino set contains 28 tiles. By systematically identifying the dominoes visible in the image, all tiles containing the number 6 are accounted for except [0,6]: [1,6] appears in row 5 as a vertical domino, [2,6] appears in row 4, [3,6] appears in row 4, [4,6] appears in row 6, [5,6] appears in row 5, and [6,6] appears in row 5. Similarly, all dominoes containing 0 are present except [0,6]: [0,0] is in row 3, [0,1] is in row 2, [0,2] is in row 4, [0,3] is in row 3, [0,4] is in row 3, and [0,5] is in row 2. Since every other domino in the standard set is visible and only [0,6] is absent, this is the missing tile.