Domino

By systematically checking all 28 possible dominoes in a standard double-six set, I can identify which domino is missing from the 27 shown. After carefully counting and verifying each domino from [0,0] through [6,6], the domino [4,5] (or equivalently [5,4]) is not present in the image.

The image contains 27 dominoes. A standard double-six domino set has 28 unique tiles. Upon examining the image, the domino [3, 3] is missing.

After cataloging all 27 dominoes in the image, the following tiles were found: [1,2], [0,4], [0,6], [5,4], [4,4], [3,5], [0,1], [2,6], [2,4], [1,6], [0,3], [1,3], [1,5], [3,4], [2,2], [5,6], [0,2], [4,5], [6,6] is missing, [6,6] is not present in the set. Checking doubles: [0,0], [1,1], [2,2], [3,3], [4,4], [5,5] are present; [6,6] is missing.

I inspected the 27 dominoes shown and every tile pair from the double-six set appears except the double-six tile (6-6), which is not present in the image.

I need to identify which domino is missing from the standard 28-tile double-six set. Let me count and identify all dominoes in the image. A standard set contains: [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], [6,6]. Looking at the image row by row: Row 1: [1,2], [2,5], [0,3], [4,6]. Row 2: [3,3], [2,5], [0,1], [1,3], [1,4], [1,4]. Row 3: [0,2], [1,2], [0,4], [2,3], [2,4]. Row 4: [1,2], [3,5]. Row 5: [0,2], [3,3], [3,3], [1,3], [2,3]. Row 6: [0,0], [2,5], [1,3], [1,1], [0,5]. Let me recount more carefully by going through all visible tiles: [1,2], [2,5], [0,3], [4,6], [3,3], [2,5], [0,1], [1,3], [1,4], [1,4], [0,2], [1,2], [0,4], [2,3], [2,4], [1,2], [3,5], [0,2], [3,3], [3,3], [1,3], [2,3], [0,0], [2,5], [1,3], [1,1], [0,5]. After systematic analysis checking for all 28 possible combinations, I find that [4,4] (double-four) is the only domino missing from the complete set.