How do I model this unique equation?

Question

I have two variables, a and b. They both start at 1. Each "round" the value of a and b doubles, then either a OR b, also increases by the original value of the other variable.

So in some round, if a and b are 8 and 5 respectively, the next round they can be either 16 and 18, or 21 and 10.

The task is, I'm given an ending value for a nd be (like a=600 and b=460), then I have to figure out the minimum number of rounds to get a and b to those totals.

Thank you.

Answer 1

For what it's worth, I wrote a program that solves this problem (through brute force). I did not use any clever mathematics, and I can't tell you how (or if) this type of problem can be solved analytically, since the recursive relationship changes each round.

I did try a = 600, b = 460 and found no solution for this case.