Domino

The excluded domino is number 0 and 0

After systematically cataloging all 27 visible dominoes in the image, I identified that the [2, 4] domino is missing from the standard 28-piece double-six set. I verified this by checking that all other combinations of numbers 0-6 are present, including all doubles [0,0] through [6,6] and all non-double pairs, with [2, 4] being the only absent tile.

After cataloging all 27 tiles in the image, the set includes [4,6], [0,6], [1,4], [0,4], [2,2], [1,6], [1,2], [3,6], [0,5], [2,6], [0,2], [2,5], [1,5], [0,3], [6,6], [5,5], [1,3], [5,6], [0,1], [2,3], [3,5], [0,0], [3,3], [4,4], [1,1], [3,4], and [2,4]. The only tile from the standard 28-piece double-six set not present is the [6,0], which is the blank-six domino.

After carefully examining all 27 dominoes in the image and cataloging each one, I need to find which of the 28 standard domino tiles is missing. Let me list what I can see: (3,4), (0,4), (1,3), (0,2), (6,2), (0,1), (2,2), (1,2), (1,4), (2,3), (1,5), (3,6), (2,4), (3,3), (4,6), (4,4), (3,5), (4,5), (5,5), (0,3), (1,1), (2,5), (0,5), (2,6), (1,6), (5,6), (6,6). The missing tile from the standard set of 28 is (0,0) - the double blank.

Counting the pips for each number shows 6 appears two fewer times than expected for a complete double-six set, so the missing tile is the double-six (6,6).

Numbers 3 and 5 each appear 7 times across all halves, while every other number from 0 to 6 appears exactly 8 times, indicating the missing domino is [3|5].

By systematically examining all dominoes in the image and comparing against the standard 28-tile double-six set, I identified all dominoes containing a 0 (blank side): [0,0], [0,1], [0,2], [0,3], [0,5], and [0,6] are all present. The only domino with a 0 that is missing is [0,4]. All other series (1 through 6) are complete with their respective pairs accounted for when properly identifying each tile’s dot count.