2 minutes

# Leetcode 2177

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 }
}
```