2177. Find Three Consecutive Integers That Sum to a Given Number

This solution is small but not the easiest to understand.

In Algebra 1, you might have learned how to sum up multiple consecutive numbers to make a result.

I came up with this solution because when writing this, I am 15, and I learned about summing up consecutive numbers 2 to 3 years ago.

The Explanation of the Solution:

x + (x + 1) + (x + 2) = num → We know that we need 3 consecutive numbers, so if x is the first number, x + 1 is the second number, and x + 2 is the third number.

3x + 3 = num → We can combine all like terms.

3x = num - 3 → Subtract 3 from both sides.

x = (num - 3) / 3 → Divide both sides by 3 to isolate x.

Now that we know the value of x, we can find the remaining two numbers, x + 1, and x + 2.

Let us take an example from the problem statment:

x + (x + 1) + (x + 2) = 33

3x + 3 = 33

3x = 30

x = 10

The first element is 10 next element is 11, and the last element is 12.

func sumOfThree(num int64) []int64 {
    if (num - 3) % 3 != 0 {
        return []int64{}
    }
    
    x := (num - 3) / 3
    return []int64{ x, x + 1, x + 2 }
}