Learned this quiz in class. Imagine that you have unlimited amounts of balls (to the left, right and bottom, NOT top). The goal is to get a ball as high as possible, moving them as you would in solitaire (You pick one ball, move it to an empty spot on the other side of a nearby ball, and remove that ball). In the pictures below, O is balls and O is empty space.
Example of a move:
You have:
OOOOOO
Pick the left ball, move it to the other side of the other ball:
OOOOOO
And remove the ball that you jumped over:
OOOOOO
I'll show the first steps: (red is the ball I'm going to move next time)
Pick a ball from the second row and move it upwards to reach the first level.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
Pick a ball as shown in the picture and move it to the empty location on the first row.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO <-- You've reached level 1
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
Pick the same ball again and move it upwards to reach the second level.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO <-- You've reached level 2
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
And so on...
Question: How high can you get a ball using this method over and over again?
(I'll give you some time to think )