### April 24, 2018

Today’s exercise is a game that mathematicians play; it comes from /u/HarryPotter5777 on Reddit:

You are given a pair of integers. You make a sequence of steps in which one member of the pair is doubled and the other is incremented by one. Your goal is to find a sequence in which the two members of the pair are equal. For instance, the sequence (1 8), (2 9), (4 10), (5 20), (10 21), (11 42), (22 43), (44 44) ends with the two numbers equal, so (1 8) is a valid starting pair.

The question is whether or not it is always possible to find a sequence, regardless of the starting pair, which makes the two numbers equal. /u/shouldertarget gives a hand-waving explanation that the answer is “Yes” later in the Reddit thread mentioned above.

Your task is to write a program that, given a starting pair, derives a sequence that makes the two numbers equal. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.