A soccer fan, upset by the defeat of his favorite team, slept restlessly. In his dream a goalkeeper was practicing in a large unfurnished room, tossing a soccer ball against the wall and then catching it.
If the ping-pong ball rolls flush against the wall, the cast-iron ball cannot crush it.
Those who know geometry can determine that if the diameter of a large ball is at least 5.83 (3+2(square root of 2) times as large as the diameter of a little ball, then the little ball will be safe if it hugs the wall.
A cast-iron ball that is larger than a soccer ball is more than 4.83 times as large in diameter as a ping-pong ball.