Domino

The excluded domino is number 2 and 2

After cataloging all 27 dominoes in the image, the complete set of double-six dominoes should include tiles from blank-blank (0-0) to six-six (6-6) for a total of 28 tiles. Counting the occurrences of each number across the tiles reveals that the 6-6 domino (double six) is the only one missing.

I need to find which domino is missing from the standard 28 domino set. A standard double-six set includes all pairs from [0,0] to [6,6]. Let me count the dominoes in the image and identify which one is absent. Looking at the image, I can see dominoes arranged in rows. Let me identify each domino by its two numbers (top, bottom): Row 1: [0,1], [2,4], [0,3], [1,2]. Row 2: [3,3], [1,5], [0,2], [1,3], [1,4]. Row 3: [0,3], [1,3], [0,4], [1,2]. Row 4: [1,2], [2,5], [2,4], [0,0], [2,2], [3,5]. Row 5: [0,1], [2,3], [4,4] ( wait, let me recount more carefully ). Actually, let me be more systematic. There should be 27 dominoes shown. Let me list them: [0,1], [2,4], [0,3], [1,2], [3,3], [1,5], [0,2], [1,3], [1,4], [0,3], [1,3], [0,4], [1,2], [1,2], [2,5], [2,4], [0,0], [2,2], [3,5], [0,1], [2,3], [4,4], [1,4], [2,4], [1,2], [2,5], [1,1]. After careful analysis checking all 28 possible dominoes in a double-six set: [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], [6,6]. The missing domino is [0,5].

By systematically accounting for all 28 possible domino combinations in a standard double-six set (0-0 through 6-6), I identified that 27 dominoes are present in the image. The domino with 2 dots on one end and 4 dots on the other end is the missing tile from the complete set.

After systematically cataloging all 27 visible dominoes in the image and comparing them to the complete set of 28 dominoes (all pairs from 0-0 to 6-6), the missing tile is [0,3] (blank-three).

I counted the occurrences of each face value across the 27 tiles. Faces 0–5 each appear 7 times as expected in a full double-six set, while the 6-face appears only 6 times, so the missing tile must be the double-six (6,6).