The sum of three consecutive integers is 1,008. What are those integers?

If they were all the same integer, then each one would be

1/3 of 1,008.

That's 336. So if they were all the same integer, they would be

336 336 336

And they would add up to 1,008.

You need them to be consecutive integers, and still add up to 1,008.

Fine! Just take one away from the first one, and glue it onto

the last one.

Now you have

335 336 337

And you haven't changed their sum.