Wednesday, January 27, 2010

Lions and Lambs

There are 17 perfectly rational lions and 1 lamb on a magical island.  Lions only eat lambs; they will not eat each other.  The magical thing about this island is that if a lion eats the lamb, it becomes the lamb by magical transformation.  The lions are very intelligent and live by two rules:
  1. Don't get eaten
  2. Eat a lamb only if it doesn't result in a violation of rule number 1.  
 A biologist observes these 17 lions and 1 lamb for a little while and then leaves for several years.  When the biologist returns, how many lions and how many lambs will remain?

Tuesday, January 19, 2010

The Scale, Parts 1 and 2

Part 1: You have 8 identical-looking gold coins; 7 are equal weight, 1 is counterfeit and slightly heavier.  Using an old-fashioned balance scale only twice, find the counterfeit coin. 

Part 2: Consider 8 gold coins again.  However, this time it is unknown whether the counterfeit coin is heavier or lighter.  You can use the scale 3 times.  Find the counterfeit coin.

Wednesday, January 13, 2010

The Egg Drop

A Phoenix Egg is best served hot. 

From Neel Tiruviluamala, via Tommy Dickie:

You've been assigned to determine how much force it takes to break a Phoenix egg and you are permitted the use of a 100-story building.  Phoenix eggs are hard and may break if dropped from the first floor or may not even break if dropped from 100th floor.  You need to find the highest floor from which the eggs will not break.  Phoenix eggs are very rare - you only have 2 identical eggs to work with.  Of course you could simply start by dropping an egg from the first floor, then the second floor, and so on until it breaks, but who has time for that?  In the worst-case scenario, in which the egg does not break even from the 100th floor, this would require 100 drops.

What strategy could you employ that requires the fewest number of drops?  Obviously the number of drops required depends on where the egg will break, so you will be judged according to the worst-case scenario.  That is to say, you will be judged according to the maximum number of drops your strategy requires.  Feel free to submit solutions to 

On Sunday, if I remember, I will provide a hint.

Wednesday, January 6, 2010

Jugs, Part 2 and a Bonus!

You're at the ocean again and you need exactly 4 gallons of water this time.  Unfortunately, all you have is an opaque 3-gallon jug and an opaque 5-gallon jug.  What will you do?

Belated Bonus:
A man walks out of his house and heads due south one mile.  He then turns left and heads due east one mile.  Finally, he turns left and heads due north one mile and arrives back home.  Who is this man?