Domino

The excluded domino is number 3 and 2

After scanning the 27 visible tiles, every pair from the 0–6 set appears except the double six; the (6,6) tile is missing.

After examining all 27 dominoes and counting the occurrences of each number from 0 to 6 across all halves, numbers 0,1,2,4,6 appear 8 times each, while 3 and 5 appear 7 times each, indicating the missing non-double domino [3,5] (with the smaller number first).

A standard double-six set has 28 unique tiles, including seven doubles ([0,0] through [6,6]). Six doubles are clearly visible in the image: [0, 0], [1, 1], [2, 2], [4, 4], [5, 5], and [6, 6]. The [3, 3] domino is the only double missing. Although visual analysis reveals several duplicates among the 27 physical tiles shown ([0, 2], [1, 2], and [1, 6]), which mathematically implies multiple unique tiles are missing (seven in total: [0, 5], [2, 4], [2, 5], [2, 6], [3, 3], [4, 5], [5, 6]), [3, 3] is the only missing piece by completion of the double-series, making it the most logical single excluded domino.

By analyzing the 27 dominoes present in the image and comparing against the complete set of 28 double-six dominoes, I identified all dominoes except for the [3,6] combination. Counting the occurrences of each number (0-6) across the visible dominoes, the number 3 appears 7 times and the number 6 appears 7 times, whereas all other numbers appear 8 times. This indicates that the missing domino contains both 3 and 6.

By systematically identifying all visible dominoes in the image and comparing them against the complete standard double-six set (28 tiles containing all pairs from 0-0 to 6-6), the domino [4, 4] is the only one missing from the collection shown.