Pythagoras liked to organize positive even integers into groups. One way he did this was to divide them into three groups: evenly-even, oddly-even, and oddly-
odd. Evenly-even numbers could be halved, halved again and again until the
number 1 was reached; oddly-even numbers could be halved but could not be
halved again; oddly-odd numbers could be halved more than once but the number
1 could never be reached. What is the sum of the least two-digit evenly-even
positive integer and the least two-digit oddly-odd positive integer? (“Halving”, in
this case, can only be carried out on even integers)