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.
