Domino

A standard double-six domino set consists of 28 unique tiles. The image shows 27 tiles. By checking off every tile present in the image against a complete list of 28 tiles (0-0 to 6-6), the missing tile is identified as [6, 4] (or [4, 6]). Tiles present: Doubles: [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6] (All 7 doubles are present) Tiles with 0: [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6] (All 6 are present) Tiles with 1: [1, 2], [1, 3], [1, 4], [1, 5], [1, 6] (All 5 extras are present) Tiles with 2: [2, 3], [2, 4], [2, 5], [2, 6] (All 4 extras are present) Tiles with 3: [3, 4], [3, 5], [3, 6] (All 3 extras are present) Tiles with 4: [4, 5], [4, 6] (Only [4, 5] is present. [4, 6] is missing) Tiles with 5: [5, 6] (Present) Therefore, the missing domino is [6, 4].

By systematically checking all 28 possible dominoes in a standard double-six set (all pairs from 0-0 to 6-6), the domino [4, 4] is the only one missing from the 27 dominoes shown in the image.

The excluded domino is number 2 and 1

I inspected each domino in the image and could not find the tile showing the pair 2 and 6; all other combinations from the double-six set are present.

After identifying all 27 dominoes in the image by counting pips in each half and sorting pairs, all combinations from the double-six set are present except [4-6]

By systematically identifying all dominoes in the image, I found tiles for all combinations of 0-6 except for the [0,4] domino. The 0-series present includes: [0,0], [0,1], [0,2], [0,3], [0,5], and [0,6]. The [0,4] tile (one side blank, other side with 4 dots in a 2x2 square pattern) is the only one from the standard double-six set that is absent.

In a standard double-six domino set, the tile [0, 0] (with no dots on both sides) is required. Counting the presence of all other tiles in the image, all except [0, 0] are present. The total number of dominoes is 27, confirming one is missing. Since the [0, 0] tile has no dots and is not visible in the image, it is the excluded domino.