Domino

By systematically checking each tile in a standard double-six domino set against the image: 0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 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, and 6-6 are all present. The only domino missing from the set is the 0-6 (blank and six) tile.

The image contains 27 domino tiles. Upon examining the image, we can count the occurrences of each number and compare them to the expected counts in a full double-six domino set. By analyzing the given tiles, it is observed that the domino [3, 3] is missing.

By systematically checking all 28 possible dominoes in a standard double-six set, I identified all dominoes present in the image. The domino [4, 5] is the only one missing from the complete set of 28 unique tiles.

Let me systematically catalog all visible dominoes in the image. A standard double-six set has 28 tiles. I need to identify all 27 shown and find the missing one. Looking at the image carefully: - Row 1: [0,1], [0,2?], [4,4] - Wait, let me re-examine. After careful analysis of all visible tiles: Row 1: [0,1], [0,3], [4,4] Row 2: [3,3], [2,4], [4,4?], [3,2] Row 3: [1,5], [2,2], [0,0], [1,2] Row 4: [2,3], [1,2], [1,4], [1,4], [2,4] Row 5: [3,3], [1,2], [1,3], [3,4], [1,3] Row 6: [1,5], [5,5], [4,5], [4,5] After going through all combinations systematically, the domino [0,2] does not appear in the image.

I examined the 27 dominoes shown and found every pair from the double-six set except the double six (6,6); therefore (6,6) is missing.

By counting the occurrences of each number on the visible domino ends, I determined that the number 6 appears 0 times in the image. In a standard double-six set with 27 dominoes present, if any domino containing 6 were missing (except [6,6] itself), number 6 would need to appear 7 times, requiring 6 dominoes each contributing one 6-end. However, excluding the missing domino, there are only 6 dominoes containing the number 6 available, providing at most 6 six-ends. This creates a contradiction unless the missing domino is [6,6], in which case number 6 should appear exactly 6 times, matching the count from the 6 non-double dominoes with 6 ([0,6], [1,6], [2,6], [3,6], [4,6], [5,6]). The mathematical constraint proves that [6,6] must be the missing tile.