Two frogs are on an eternal stairway. Will they ever be able to meet?
Anton is on step 14 and jumps 4 steps. Billy is on step 16 and jumps 6 steps.
The way I look at this is that as long as they're not on the same step, the one on the lowest jumps next, so:
- Their difference (Anton-Billy) is -2
- Anton jumps to step 18, difference = 2
- Billy jumps to step 22, difference = -4
- Anton jumps to step 22 - THEY MEET
If Anton had been on step 15 instead:
- Their difference is -1
- Anton jumps to step 19, difference is 3
- Billy jumps to step 22, difference is -3
- Anton jumps to step 23, difference is -1
- Since the difference has repeated, they will never meet
However, I am certain there's a much better way to find out if and where they will ever meet in a single equation.