The Camels

Borrowed from http://www.folj.com/puzzles/

Four tasmanian camels traveling on a very narrow ledge encounter four tasmanian camels coming the other way.

Tasmanian camels never go backwards, especially when on a precarious ledge. The camels will climb over each other, but only if there is a camel sized space on the other side.

The camels didn't see each other until there was only exactly one camel's width between the two groups.

How can all camels pass, allowing both groups to go on their way, without any camel reversing?

Hint: to help visualize, use paper clips or coins.  

Apples and Oranges

This also came from Wu Riddles. 

There are three closed and opaque cardboard boxes. One is labeled "APPLES", another is labeled "ORANGES", and the last is labeled "APPLES AND ORANGES". You know that the labels are currently misarranged, such that no box is correctly labeled. You would like to correctly rearrange these labels. To accomplish this, you may see only one fruit from one of the boxes. Which box do you choose, and how do you then proceed to rearrange the labels?

The Yukiad Contraption

Thanks to Jon Campbell for telling me about this one, found at Steven Landsburg's blog, The Big Questions.  The original puzzle is from the novel The Yukiad, by David Snaith. 


Consider a  glass contraption—a perpetual motion machine, really—consisting of a clear glass hula hoop on the ground containing several colored beads, which travel through the hoop, some clockwise, some counterclockwise, all at the same speed, bouncing off each other in perfectly elastic collisions whenever they collide. Whenever two beads collide, they instantly bounce off each other and proceed in the opposite of their original directions, still at the same speed. Take a snapshot of this system at, say, 12PM. Must there be some time in the future when another snapshot of the system will look identical? In other words, does the history of the system repeat itself?

(Hint: for simplicity, start with a few beads, then generalize)

Cut the Cake

Happy Birthday, Kyle! 
With 3 straight cuts through a cylindrical cake, make 8 equal-sized slices. 

There are two solutions.

(Hint: you are allowed to move some or all of the cake)

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).

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.

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?