Domino

The excluded domino is number 2 and 1

After systematically checking all 28 possible dominoes in a standard double-six set, the domino [1,1] (double one) is the only one missing from the 27 dominoes shown in the image. All other combinations from [0,0] through [6,6] are present.

I analyzed the image and identified 27 dominoes. A standard double-six domino set consists of 28 tiles. By cataloging the pairs present (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), I determined that the [6, 6] tile (double-six) is the only one missing.

I counted the pips on each domino half in the image and found that all numbers 0–6 appear the expected number of times except 2 and 4, which each appear one time fewer than they should. Therefore the missing domino is [2,4].

By analyzing the frequency of each number (0-6) appearing on the domino halves in the image, I count 7 occurrences of the number 0 and 7 occurrences of the number 6. In a complete double-six set, each number should appear exactly 8 times across the 28 dominoes (each number appears in 7 dominoes, with the double counting as two occurrences). Since there are 27 dominoes shown, one is missing. The missing domino must account for one missing ’0’ and one missing ’6’, indicating the excluded domino is [0,6]. Verifying the visible dominoes with 0: [0,0], [0,1], [0,2], [0,3], [0,4], [0,5] are all present, confirming [0,6] is the only one missing.