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

Feb 9, 2016

$69$, $71$, and $73$

Explanation:

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

$x + x + 2 + x + 4 = 3 x + 6$

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

Subtract 6:
$3 x = 201$

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 $213$.