Sunday, December 21, 2014

349: Hole-in-One Insurance

If the average golfer is able to get a hole-in-one once in approximately 3000 rounds of golf (18 holes apiece), then what is the probability of any one of 100 average golfers getting a hole-in-one on the 5th hole during the weekend golf tournament?

What's the best way to find this out if you're the insurance company that will write this policy?

Saturday, December 20, 2014

348: Homer's Pythagorean proposition


$1782^{12}+1841^{12}=1922^{12}$

Wait, didn't Fermat say this was impossible?
What's a three-second way to tell that this equation is false?

Friday, December 19, 2014

347: Combinatorics

Consider eight objects. We will choose them one at a time, two at a time, three at a time, and so on.

Which of these will result in identical numbers of ways?
Why?

Thursday, December 18, 2014

346: Casting the Play

The cast of a school play that requires 4 girls and 3 boys is to be selected from 7 eligible girls and 9 eligible boys.

  • Will it be a different calculation if the boys are willing to play girls' parts, as in Shakespeare's time? If so, how will it be different?

Wednesday, December 17, 2014

345: Fair or Foul?

Sullivan bought a die at the magic shop. He rolls it 155 times and gets the following results:
  • ONE: twenty-eight times
  • TWO: twenty times
  • THREE: fifteen times
  • FOUR: thirty-one times
  • FIVE: thirty-two times
  • SIX: twenty-nine times.
Is this die loaded?
What is the probability he will get a 6 on the next roll?

Tuesday, December 16, 2014

344: Monty Hall

Once upon a time, the world's smartest person (Marilyn vos Savant, IQ: 228) received a question for her newspaper column …
 Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker, Columbia, MD

Marilyn's answer was surprising to many people. What do you think?

Wednesday, December 10, 2014

343: Forces and Friction

Your teenage son has a fast car.


He knows that friction is determined by the weight of the car over the wheels, the "normal" force. He also knows that additional weight means that the car can't accelerate as fast, but he's also having problems with the rear tires spinning out.  He's convinced that having Fat Eddie sit in the back will help his quarter-mile time.

 Will the extra weight help him or hurt him?