What is the sum of two consecutive integers is less than 83. find the pair of integers with the greatest sum

Well, the sum has to be less than 83.  Do you think maybe it could be 82 ? ?
Sadly, it couldn't be 82.  If two integers are consecutive, then one is even and
one is odd, and their sum is always odd.  So the greatest sum less than 83
is going to be 81 .

Since the integers are consecutive, both of them have to be right around
half of 81 .  Half of  81  is (40 and 1/2), so let's try  40  and  41 :

40 + 41 = 81       That's it !       yay!