Domino

The excluded domino is number 2 and 1

By systematically checking all 28 possible domino combinations in a standard double-six set (all pairs from 0-6 including doubles), the domino [4, 4] is the only one not visible in the image. All other dominoes including [0,0], [1,1], [2,2], [3,3], [5,5], [6,6] and all non-double combinations appear to be present.

After cataloging all visible dominoes in the image, I identified the following tiles: [0,2], [0,0], [2,4], [1,2], [2,5], [2,6], [1,6], [0,1], [1,4], [0,4], [3,4], [2,2], [1,3], [2,3], [3,6], [3,5], [3,3], [1,1], [1,5], [4,6], [4,5], [4,4], [1,6], [5,6], [2,6], [5,5], [6,6]. Comparing against a full standard set of 28 dominoes (all combinations from [0,0] to [6,6]), the missing domino is [0,3].

By carefully examining the ASCII art representation of the 27 dominoes and counting the dot patterns in each half of every tile, all standard double-six dominoes are present except for [4,6]. The occurrences of each number confirm that 4 and 6 appear 7 times each, while others appear 8 times.

I identified all 27 dominoes present in the image by systematically counting the dots on each tile. The complete double-six set contains 28 dominoes. By checking which dominoes with 5-pips were present, I found [0,5], [1,5], [2,5], [3,5], [5,5], and [5,6]. The domino [4,5] (with 4 dots on one side and 5 dots on the other) was not found in the image, indicating it is the excluded tile.