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{1, 2}, {7, 8} and {10, 11}.

The triangular numbers are 1, 3, 6, 10, 15, 21, 28, ...

The sum of two adjacent numbers is odd, so adjacent numbers that sum to 1, 3, 15, 21 are the solution.

1 is impossible, leaving 3, 15 & 21 as possible sums, giving the adjacent numbers {1, 2}, {7, 8} & {10, 11}

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Q: What are adjacent number in a clock whose sum is triangle number?
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