Question

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

Answer 1

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!