Domino

The excluded domino is number 2 and 1

After cataloging all 27 dominoes in the image and comparing them against a standard double-six set, the [0, 6] (blank and six) tile is the only one missing from the complete 28-tile set.

By systematically analyzing all 27 dominoes visible in the image and cross-referencing against the complete set of 28 unique domino combinations (all pairs from 0-6), the domino [2,4] is not present. The visible dominoes account for all other combinations, making [2,4] the missing tile from the standard double-six set.

The missing domino is [1,1]

After counting the occurrences of each number across all halves in the 27 dominoes shown, numbers 5 and 6 each appear 7 times, while all others appear 8 times, indicating the missing domino is [5,6].

Counting the pips for each face value across the 27 visible tiles shows the count for the value 5 is two fewer than the expected 8 pips (while all other values appear the expected number). That deficit of two indicates the missing tile is the double-five (5,5).

A standard double-six set contains 28 dominoes where each number 0-6 appears exactly 8 times across all domino halves. By analyzing the 27 dominoes in the image: The number 0 appears in [0,0] (twice), [0,1], [0,2], [0,3], [0,4], and [0,5] - totaling 7 occurrences. The number 6 appears in the vertical [6,6] domino on the left side (twice) and in five other dominoes: [1,6], [2,6], [3,6], [4,6], and [5,6] - totaling 7 occurrences. Since both 0 and 6 appear 7 times (one less than the expected 8), and [0,6] is the only domino containing both numbers, it must be the missing domino. All other dominoes in the 0-series are accounted for, and [6,6] is present as the vertical tile.