For the floating ball problem, I had the same intuition as Bucky: A floating object will displace its own weight in water, so we can replace the ball with an amount of water that exactly fills in the hole created by the submerged part of the ball. So the box is balanced no matter where you move the ball to.
“Thinking Physics” by Epstein is an excellent source for puzzles like this, where you identify the relevant physical principles to give qualitative answers as opposed to doing tedious calculations.
Wow, excellent post!
For the floating ball problem, I had the same intuition as Bucky: A floating object will displace its own weight in water, so we can replace the ball with an amount of water that exactly fills in the hole created by the submerged part of the ball. So the box is balanced no matter where you move the ball to.
“Thinking Physics” by Epstein is an excellent source for puzzles like this, where you identify the relevant physical principles to give qualitative answers as opposed to doing tedious calculations.