Sorry, add 23 to what?
72 = -22 + (-21) + .... + 0 + ..... + (x - 1) + x .... (A)
Reverse the order:
72 = x + (x - 1) + ..... + 0 + ..... + (-21) + (-22) .... (B)
Add (A) and (B) together:
144 = (x - 22) + (x - 22) + ..... + (x - 22) + (x - 22).
There are 23 + x identical terms on the right. Therefore:
144 = (x - 22)(23 + x).
Solve for x (you can do that, right?) and keep the positive solution. I get x = 25.
It's a trick I learned from Carl Gauss. If you want, you can read about him here: Carl Friedrich Gauss - Wikipedia, the free encyclopedia. He's a bit famous in certain circles .....
He is awesome. I have his Disquisitiones Arithmeticae, very beautiful book