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)