Wednesday, March 31, 2010

The Prisoner, the Liar, and the Truth, Part II: Enter the Other Guy

Recall from a couple weeks ago, the door that leads to the electric chair in the Prison for Creative and Unusual Punishment.  It is located in a depressing, windowless basement hallway near the back, right next to an identical door that leads to an unguarded fire exit.

A prisoner with similar lamentable circumstances to the guy in part 1 was being brought in for execution, and the warden wanted to give him one last chance at freedom.  This time, however, would be more complicated.  Rather than two guards, there were three guards with them, named Al, Bob, and Carl.  The warden held a brief huddle with the three guards, out of earshot of the prisoner.  He then told the prisoner some of what went down in the huddle. 

"I've instructed one guard to tell nothing but lies when asked a yes-or-no question.  I've instructed another guard to tell only the truth when asked a yes-or-no question.  I then repeated one of those two instructions to the remaining guard.  Unfortunately, I'm not going to tell you whether there are two liars an a truth-teller, or two truth-tellers and a liar.  And I'm certainly not going to tell you which is which.  You have two yes-or-no questions to ask, choosing one guard at a time to respond (no asking a question of the whole crowd).  From the information you glean, you may choose a door.  Best of luck."

What two yes-or-no questions can the prisoner ask whose answers will lead him to freedom?

Please submit answers in the comments section of the blog, or to me directly (no spoilers in Google Buzz).

Monday, March 29, 2010

The Catenary Chain

This week's post on Steve Strogatz's New York Times column reminded me of this puzzle.  In it he re-explains math in a creative and intuitive way, from basic counting through imaginary numbers, functions, and more.  The post reminded me of this because in it he talks about how mathematical functions can explain every-day shapes, such as how water at a drinking fountain forms a parabola.  A hanging chain forms a catenary, but its shape can be approximated with a parabola.  It is a great new one I found at Wu Riddles, and apparently it originated at a Microsoft Interview.  BUT: don't be intimidated by all the math, I have faith that you can solve this one. 

You have a 6-foot long chain that is suspended at its ends, tacked to a wall. The tacks are parallel to the floor. Due to gravity, the middle part of the chain hangs down below the ends, forming a 'U'-type shape; the height of this 'U' is 3 feet from top to bottom. Find the distance in between the tacks.

Wednesday, March 17, 2010

The Prisoner, the Liar, and the Truth

The door that leads to the electric chair in the Prison for Creative and Unusual Punishment is located in a depressing, windowless basement hallway near the back.  It just so happens that it is right next to an identical door that leads to an unguarded fire exit. 

One day the warden was bringing a prisoner to be executed, but was feeling sorry for him.  The prisoner had been convicted on dubious charges and DNA evidence had been unearthed that might have exonerated him, but the court threw it out.  So the warden wanted to give the prisoner one more chance at freedom.  There were two guards with them and the warden whispered in their ears, out of earshot of the prisoner.  The warden instructed one to tell nothing but lies when asked a yes-or-no question and the other to tell only the truth when asked a yes-or-no question.  Otherwise they were to remain silent.  The prisoner couldn't tell which was the liar and which was the truth-teller. 

The warden then told the prisoner that he could ask one yes-or-no question to one of the guards.  If, from the answer, he could pick the correct door to freedom, the guards would look the other way. 

What question should the prisoner ask?

Wednesday, March 10, 2010

Brothers and Sisters, I Have None

This is one of the first riddles I was able to remember consistently and I got it from my Dad.  A man looks at a portrait and says, "Brothers and sisters, I have none.  But that man's father is my father's son."  What is the relationship of the man in the portrait to the speaker? 

Tuesday, March 9, 2010

Solution to the Scale, Part 3 is up

I remembered the solution to the scale riddle with 12 weights and only 3 weigh-ins.  It's located in the expanded "The Scale, Part 3" post. 

The Scale, Part 3

Told to me by Tommy Dickie:

This time you have 12 identical-looking gold coins.  11 are equal weight, 1 is counterfeit and you don't know whether it's heavier or lighter than the others.  Using an old-fashioned balance scale only three (3) times, find the counterfeit coin and determine whether it is lighter or heavier than the others.  

Wednesday, March 3, 2010

The Monks

There are 40 monks living on a deserted island, at the foot of a mountain with a monastery at the top. Each monk has either blue or green eyes--there is at least one monk of each eye color, but none of them knows which color he has. They can see each other's eyes, but cannot in any way communicate to each other anyone's eye color (ie, everyone knows everyone ELSE's eye color, but not their own). They gather every day for supper, but otherwise spend their time alone in their individual secluded huts. One day, God appears and tells them all that green-eyed monks are welcome to hike up the mountain to the monastery; but ONLY green-eyed monks are allowed. He says that one morning, every green-eyed monk will wake up knowing that he is a green-eyed monk, and when that day comes, they will each ascend the mountain during sunrise, leaving just the blue-eyed monks to gather for supper later that day. This does indeed happen. How do the green-eyed monks accomplish this?

Sorry for the Delay

I'm sorry I didn't post anything last week. To compensate, I offer two riddles: one easy, one hard. I guess the easy one is whichever you get first. Feel free to post ideas in the comments section.

The first I got from Wu Riddles and the second from Tommy Dickie. The second is similar to a riddle about cheating husbands.

The Penny, the Cork, and the Bottle

Take a penny, an empty wine bottle, and a cork.  Put the penny in the wine bottle and cork the bottle.  Now remove the penny without pulling out the cork and without breaking the cork or bottle.