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.
Bob suggested that Dave hold his finger in the air while someone wound a piece of string tightly around his finger just above the metal ring. The string forced the swelling down. As they unwounded the string from the end nearest the ring, someone else slid the ring up. They continued winding and unwinding the string until the ring could be easily removed.
The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!). Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!...