Question

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)

Answer 1

The least two-digit evenly-even integer is 16, and the least two-digit oddly-odd integer is 10. Their sum is 26.

Step-by-step explanation:

The question involves categorizing positive even integers into three types as described by a hypothetical scenario involving Pythagorean ideas: evenly-even, oddly-even, and oddly-odd. To answer this question, we need to identify the least two-digit numbers for both evenly-even and oddly-odd integers according to the rules provided.

An evenly-even number is one that can be divided by two repeatedly until it becomes 1. The smallest two-digit evenly-even number is 16 (divided by 2 gives 8, then 4, then 2, then 1).

An oddly-odd number is an even number that can be halved more than once but never reaches the number 1. The smallest two-digit oddly-odd number is 10 (divided by 2 gives 5, and 5 is not even, hence cannot be halved further).

The sum of the least two-digit evenly-even positive integer (16) and the least two-digit oddly-odd positive integer (10) is 26.