Wednesday, November 25, 2009

The Fuses

This is a two-part riddle.

Part 1: You have two irregular string fuses.  They burn unevenly, at unpredictable rates (slow, then fast, then maybe slow again - you don't know).  The one thing you DO know is that when either one is lit at one end, it will burn for exactly one hour.  So if you lit one, then the other in sequence, you would be able to measure out two hours.  As it turns out, however, you need to measure exactly 90 minutes.  The fuses can only be lit on the ends - not in the middle - and all you have is the fuses and a lighter.  How do you get an hour and a half?

Part 2: Using another pair of the same kind of 1-hour string fuses, how do you get 45 minutes?

Wednesday, November 18, 2009

The Prisoners and the Light Switch

The warden at the Prison for Creative and Unusual Punishment places a high value on intelligence, believing that intelligent people should be integrated into society no matter what their past misdeeds.  So rather than holding parole hearings, the warden routinely subjects his prisoners to tests of intelligence.  If they pass they are set free.  If they fail, they are usually executed.

For the next test, each of 20 prisoners will be placed in solitary confinement.  Every once in a while, a prisoner's name will get drawn from a hat and he will get to visit the Rec Room.  The Rec Room is no different from any of the barren concrete confinement cells except it has a light switch on the wall that isn't wired to anything.  The prisoner is allowed to flip that switch to his heart's content for a minute, then has to go back to solitary.  Then after another random length of time - maybe 5 minutes, maybe 5 days or more, another random prisoner will get selected to go to the Rec Room.  Note that the same prisoner might be selected multiple times in a row.  This will continue until a prisoner can tell a guard that everyone has been to the Rec Room at least once.  At that point, all of the prisoners will be set free.  If he's wrong, though, everyone will get executed.

So before the test happens, the 20 prisoners get to have one last party/meeting to coordinate how they are going to have someone know when everyone has been to the Rec Room.  After this meeting, however, there will be no communication between them.  What should they do?

Addendum: This riddle can be separated into two parts, with two similar solutions.  First, come up with a strategy assuming that the switch starts in the 'off' position and that everyone knows it.  Then for an additional challenge,  assume that the initial position of the switch is unknown.  (Thanks to Adam Sigelman for reminding me).

The Milk and the Tea

Consider two identical cups, one half-full of tea, the other half-full of milk.  You take a teaspoon of milk from the milk cup and put it in the tea cup.  Then you take a spoonful out of the tea cup and put it in the milk cup.  Now: is there more tea in the milk cup, or more milk in the tea cup? 

The Jugs and the Ocean

You're at the beach and you have two opaque jugs. One holds 13 gallons, the other holds 7. For whatever reason, you need exactly 2 gallons. You have no other containers. How do you do it?