How many functions f: {1, 2, 3, 4} - {5, 6, 7, 8} satisfy the condition that f(1) + f(2) + f(3) + f(4) is an odd number?

Question

How many functions f: {1, 2, 3, 4} -> {5, 6, 7, 8} satisfy the condition that f(1) + f(2) + f(3) + f(4) is an odd number?

Accepted Answer

128. Since exactly half of the values in {5,6,7,8} are odd and half even, by symmetry exactly half of all 4⁴ = 256 functions produce an odd sum, giving 128 functions.

How many functions f: {1, 2, 3, 4} -> {5, 6, 7, 8} satisfy the condition that f(1) + f(2) + f(3) + f(4) is an odd number?

Solution

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