Domino

The excluded domino is number 0 and 0

After listing all 28 possible tiles in a double-six set and comparing them to those present in the image (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), the triple-six (6-6) tile is missing.

By systematically checking all 28 possible dominoes in a standard double-six set (all pairs from 0-0 to 6-6), I identified 27 dominoes present in the image. The domino [4, 4] (double-four, showing four dots on both sides) is the only one missing from the complete set.

I inspected the 27 visible tiles and found all standard double-six tiles except the double-six; no tile shows six pips on both ends, so the missing tile is [6,6].

After analyzing the image and counting the occurrences of each number across all halves of the 27 dominoes, the numbers 4 and 5 each appear 7 times, whereas all other numbers from 0 to 6 appear exactly 8 times. This indicates that the missing domino is the [4|5] tile.

By analyzing the visible dominoes in the image and comparing against the complete set of 28 double-six dominoes, the missing domino is [0,5]. I identified all other dominoes involving the number 5: [5,6], [2,5], [3,5], [4,5], [1,5], and [5,5] are all present. For the number 0, I identified [0,1], [0,3], and [0,4]. The only domino that completes the set while satisfying the constraint that number 5 must pair with 0 is [0,5].