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To find the number of 3-digit numbers where the sum of the digits equals 8, we can denote the digits as (a), (b), and (c) (where (a) is the hundreds digit, (b) is the tens digit, and (c) is the units digit). The equation we need to solve is (a + b + c = 8) with the constraints (1 \leq a \leq 9) and (0 \leq b, c \leq 9). By changing variables (letting (a' = a - 1)), we can rewrite the equation as (a' + b + c = 7) with (0 \leq a' \leq 8). The number of non-negative integer solutions to this equation can be found using the stars and bars method, yielding a total of (36) valid combinations. Thus, there are 36 three-digit numbers whose digits sum to 8.

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3mo ago

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