For any set of numbers n-1, n, and n+1, the average will be n. For example, if the numbers are 18, 19, 20, the average will be 19.
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19, 20, 21
There are no three consecutive numbers that are squares. Otherwise, there are an infinite sets of squares of three consecutive numbers: for example, {1,4,9}, or {4,9,16} or {576, 625, 676}
The three consecutive odd prime numbers are 3, 5, and 7.
The numbers are 8, 9 and 10.
There is no set of three consecutive numbers totaling 170.