PUZZLERS

A. Two trains are 120 miles apart (stop me if you’ve heard this before). They are traveling toward each other at 60 miles an hour. A bee is flying back and forth from the headlight of one train to the headlight of the other train at 120 miles an hour. So the bee’s path is a diminishing zig-zag until the two trains collide. Question: how far does the bee travel?

You can solve this by brute force… add up the diminishing paths of the bee buzzing back and forth. Or you can realize that if the trains collide in one hour, and the bee is traveling at 120 miles per hour, then its total travel distance is 120 miles! Cool. Physics is like this.

​B. Now think about this: is the infinity of integers a larger infinity than the infinity of infinitesimals between 0.00000 and 1.00000? Or smaller? If you need a hint, drop me line.

C. If a bottle that starts off empty with one bacterium that doubles every second becomes full in one hour, how long will it take to be half full? (Hint: not a half hour.)

D. Here’s a frivolous diversion. It’s well known that a cat, when dropped, will always land on her feet. It’s also well known that a slice of toast, if slipped off a table, will always land on the buttered side down. So here’s the question: if you strap a slice of buttered toast on the back of a cat (buttered side up) and drop the combo, which way will it land?

E. Now: a shrewd brain teaser. A guy is sitting in a rowboat in pool. He has a huge rock in the rowboat. He drops it overboard. Question: does the water level in the pool rise, fall, or stay the same? (J. Robert Oppenheimer and I both got this one wrong.)

F. Lewis Carroll wrote “Alice In Wonderland” He was also a mathematician (Charles Dodson?) He devised this puzzler: You are given two wine glasses. They are equal in size. One glass contains red wine. The other contains white wine. The amount of red wine equals the amount of white wine. Now, you take a teaspoon of the red wine and transfer it to the white wine glass. You stir the mixture. You then dip the teaspoon on the mixture and take a teaspoon of the mixture and transfer it to the red wine glass. Here’s the question: is there as much red wine in the white wine glass as there is white wine in the red wine glass? Contact me if you need help.

G. Ping Pong Ball Bounce? A magician claims to be able to throw a Ping Pong ball so that it would go short distance, come to a dead stop, and then reverse itself. He added that he would not accomplish this by bouncing its off a wall or any object or tying anything to it or by giving it spin. How could he do this? If the magician throws the ball upward into the air, not horizontally, its motion will be reversed by gravity — not by a collision with the ground, a table, or a wall.

H. Twin Paradox? Marsha and Marjorie were born on the same day of the same month of the same year to the same mother, yet they are not twins. How is this possible? Marsha and Marjorie are triplets.

PUZZLERS

A. Two trains are 120 miles apart (stop me if you’ve heard this before). They are traveling toward each other at 60 miles an hour. A bee is flying back and forth from the headlight of one train to the headlight of the other train at 120 miles an hour. So the bee’s path is a diminishing zig-zag until the two trains collide. Question: how far does the bee travel?

You can solve this by brute force… add up the diminishing paths of the bee buzzing back and forth. Or you can realize that if the trains collide in one hour, and the bee is traveling at 120 miles per hour, then its total travel distance is 120 miles! Cool. Physics is like this.

​B. Now think about this: is the infinity of integers a larger infinity than the infinity of infinitesimals between 0.00000 and 1.00000? Or smaller? If you need a hint, drop me line.

C. If a bottle that starts off empty with one bacterium that doubles every second becomes full in one hour, how long will it take to be half full? (Hint: not a half hour.)

D. Here’s a frivolous diversion. It’s well known that a cat, when dropped, will always land on her feet. It’s also well known that a slice of toast, if slipped off a table, will always land on the buttered side down. So here’s the question: if you strap a slice of buttered toast on the back of a cat (buttered side up) and drop the combo, which way will it land?

E. Now: a shrewd brain teaser. A guy is sitting in a rowboat in pool. He has a huge rock in the rowboat. He drops it overboard. Question: does the water level in the pool rise, fall, or stay the same? (J. Robert Oppenheimer and I both got this one wrong.)

F. Lewis Carroll wrote “Alice In Wonderland” He was also a mathematician (Charles Dodson?) He devised this puzzler: You are given two wine glasses. They are equal in size. One glass contains red wine. The other contains white wine. The amount of red wine equals the amount of white wine. Now, you take a teaspoon of the red wine and transfer it to the white wine glass. You stir the mixture. You then dip the teaspoon on the mixture and take a teaspoon of the mixture and transfer it to the red wine glass. Here’s the question: is there as much red wine in the white wine glass as there is white wine in the red wine glass? Contact me if you need help.

G. Ping Pong Ball Bounce? A magician claims to be able to throw a Ping Pong ball so that it would go short distance, come to a dead stop, and then reverse itself. He added that he would not accomplish this by bouncing its off a wall or any object or tying anything to it or by giving it spin. How could he do this? If the magician throws the ball upward into the air, not horizontally, its motion will be reversed by gravity — not by a collision with the ground, a table, or a wall.

H. Twin Paradox? Marsha and Marjorie were born on the same day of the same month of the same year to the same mother, yet they are not twins. How is this possible? Marsha and Marjorie are triplets.