March 2010
9 posts
Wanna Play?
I offer to play a card game with you using a normal deck of 52 cards. the rules of the game are that we will turn over two cards at a time. if the cards are both black, they go into my pile. if they are both red, they go into your pile. if there is one red and one black, they go into the discard pile.
We repeat the two card flipping until we’ve gone through all 52 cards. whoever has...
Crazy Guy on the Airplane
A line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let’s say that the nth passenger in line has a ticket for the seat number n.)
Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite...
Chameleons
At one point, a remote island’s population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) is it ever possible for all chameleons to become the same color? why or why...
Railroad Bridge
A man needs to go through a train tunnel. He starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him. you don’t know how far away the train is, or how fast it is going, (or how fast he is going). All you know is:
if the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the...
Cars on the Road
if the probability of observing a car in 20 minutes on a highway is 609/625, what is the probability of observing a car in 5 minutes (assuming constant default probability)?
Solution
I haven’t written up a solution for this yet, but smarter people than I have described some on the discussion forum.
You can read their thoughts here.
Switches
The warden meets with 23 new prisoners when they arrive. He tells them, “You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.
“In the prison is a switch room, which contains two light switches labeled A and B, each of which can be in either the ‘on’ or the ‘off’ position. I am...
Yarr Maties
Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their years of service, Pirate 5 having five years of service, Pirate 4 four years, and so on down to Pirate 1 with only one year of deck scrubbing under his belt. To divide up the loot, they agree on the following:
The most senior pirate will propose a distribution of the booty. All pirates will then vote, including...
The Oldest Plays the Piano
Two MIT math grads bump into each other while shopping at Fry’s. They haven’t seen each other in over 20 years.
First grad to the second: “How have you been?” Second: “Great! I got married and I have three daughters now.” First: “Really? How old are they?” Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the...
The Rope Bridge
Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time.
Each of the campers walks at a different speed. One can cross the bridge in 1 minute,...
