Question

The sum of three consecutive odd numbers is more than 207, how do you find the minimum values of these integers?

Answer 1

`69`, `71`, and `73`

Explanation:

First odd: `x`
Second odd: `x + 2` (2 greater than the first, to skip the even number in between
Third odd: `x + 4`

Add all three:
`x + x + 2 + x + 4 = 3x + 6`

Now let's set it to 207:
`3x + 6 = 207`

Subtract 6:
`3x = 201`

Divide by 3:
`x = 67`

So our numbers are
`x = 67`
`x + 2 = 69`
`x + 4 = 71`

....

Not so fast!

`67 + 69 + 71 = 207`, but we need numbers that are greater than `207`!

That's easy, we just need to move the lowest odd (`67`) to be just more than higheset odd (`71`). This makes our values:

`69`, `71`, and `73`, which sum to `213`.