BBQ ‘em if you’ve got ‘em…

Today is Memorial Day, where we honor our military casualties by not working and (hopefully) barbecuing. For every Memorial Day weekend that I can remember my grandmother has traveled to her family’s old stomping grounds in Indiana to place flowers on the graves of all of her deceased family members, military or not.

For many of us, the day is more leisurely, and so I thought it would be worthwhile to recommend Chronotron — a time-themed distraction that I have found to be quite enjoyable. In the game you use a time machine to create multiple instances of yourself in order to solve a puzzle.

Water Water Everywhere

Think about how much water you think is on Earth. If you were to take it all and form it into a sphere, how big do you think it would be? Now do the same with all the air on Earth.

Dan Phiffer has a picture of what that would look like, courtesy of the Science Photo Library.

A Really Big Number

This week’s Car Talk puzzler has me stumped.

A student is asked if the following number is a perfect square: 334,912,740,121,562. Crusty knows the answer immediately. What does Crusty know?

Music Charts

This couldn’t wait until Music Monday.

1. Choose a song.
2. Find a mathematical way to express the meaning of the song.
3. Create a chart.

Lunch Time! the Puzzle

 I thought this on-line puzzle was a lot of fun, and definitely fit with our theme… or is it a motif?

 Just don’t look too close at the picture to the left…

Puzzle: The Lonely Barber

One of the great things about Car Talk on NPR is the Weekly Puzzler. Sometimes they’re car puzzles, sometimes they’re math/logic puzzles, and sometimes they’re just straight-up riddles. I was intrigued by this week’s:

One Horse, NV has one barber in the whole town. For some reason, one of the laws in the town is that every man in town must be clean-shaven. Further, every man either must shave himself or be shaven by the barber, and the barber may only shave those that don’t shave themselves. So, the question is: who shaves the barber?

I think I have an answer, but I don’t know if I’m making it overly difficult for myself. In any case, we’ll find out the answer on tomorrow’s program.

Free Energy!

British scientists claim to have a device that outputs more energy than is input. Alright, Team Lunchtime!, you’re on the case!

A puzzle to pass the time

Here’s something to work on if you have nothing better to do, or if you do have something better to do, but want to do this anyway.

There is a staircase with 100 stairs. You are given two glass balls and the task of determining which is the highest step they can be dropped from without breaking. What is the optimum method for determining this step?

Additional rules and clarifications.
1. The only experiment you may do is dropping the balls from a step and seeing whether they break.
2. Optimum in this case is defined as performing the least number of tests in the worst case scenario.
3. No matter what step the ball is dropped from it falls all the way to the bottom of the staircase.
4. If the ball breaks at step N, it breaks at all higher steps.
5. Once a ball is broken, it cannot be used in further tests. So if you break both balls without determining the answer, you lose.

If this puzzle was too easy for you, you can try the case where there are N stairs, or M balls, or both. I haven’t done these general cases, so I don’t know how hard they might be.

Juggling off the weight

There is a popular riddle that you may have heard about traveling in a boat with 3 heavy balls such that the total weight is more than the boat can handle. The “solution” is to juggle the balls so that one is always in the air, which will make the total weight low enough for the boat to handle.

When I heard this riddle as a kid I though it was very clever. Once I had learned some physics I began to wonder if it was really accurate. Once I had a decent intuition, it struck me that this idea could never work. But it wasn’t until this morning that I actually calculated anything — I think I had a dream about this last night that inspired this activity.

Heuristic #1: When you’re juggling, you have to apply an upward force to the ball to throw it and during this time the ball is perceived as heavier. The same goes for stopping the ball when you catch it. The fact that the ball in the air contributes nothing is counteracted by these other two forces.

Heuristic #2: The boat with the traveler and the balls is a closed system. It can’t get lighter unless it’s acted on by an outside force. This trick is like picking yourself up off the ground.

I’m pretty sure someone taking a freshman physics class would have the tools to bust this riddle. Imagine a piston that periodically launches and catches a ball. It’s straightforward to calculate the perceived weight of the ball during launching and catching and, including the zero weight during the flight of the ball, find that the time averaged weight of the ball is just the gravitational weight.