On a melancholy spring evening, you doze off. When you wake up, you find yourself in mathematical utopia - every plane surface is perfectly plane, and ever sphere perfect. In front of you is a perfectly vertical wall that is exactly perpendicular to the infinite plane that you are standing on. On the wall, there is a strange shelf, and lying around are exactly
six seven spherical balls of lead. You pick up the one on the ground and ponder about what you’re seeing. The wall is shown in the diagram below.
You note the date, and it is April 1, 2019. You realise that if you find what the thing in front of you means, you’ll be able to cause a new renaissance in your own world when you wake up. It’s not long before you are snatched out of this utopia, this Garden of Euler - so think fast!
Oh yes, this world is non-ideal in one way - every collision is completely inelastic.