The Glass

You have a perfectly cylindrical glass completely full of water (no rounded edges on the bottom, same diameter all the way down).  How do you empty out exactly half of the water?  There are no markings on the glass and you have nothing else to work with.

2 Ant Riddles

1. An ant is on the corner of the floor of a perfectly cubic empty room and wants to get to the farthest corner of the room, on the ceiling.  What is the shortest route?
2. Four ants are on each corner of a square, 2x2" Post-It note.  Each ant is facing the ant immediately to his left.  All four ants begin marching at once, each aiming for the ant immediately to his left.  Eventually the four ants spiral into the middle of the Post-It note, where they meet.  How far does each ant travel?

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?

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.

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 charlesdguthrie@gmail.com. 

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

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?

The Gold Coins

For Christmas this year, the king of Florin received 10 bags of identical gold coins from the king of the neighboring country of Guilder.  Each bag contains 100 gold coins and the coins weigh 1 ounce each.  However, he was tipped off that one of the bags was switched out in transit with a bag of 1.1-oz. counterfeit coins.

Florinese technology is very limited, so the king's digital scale, accurate to the nearest tenth of an ounce, can be used only once.  How can a weigh-in be arranged that will identify the counterfeit bag?