Dots and Rows

This is an old one my dad told me, though I've also heard it as a CarTalk puzzler before:

Above is a straight row of 4 dots: it is a 4-dot row.
Next, we have a set of 13 dots that creates 5 different 4-dot rows.

 

Now again create 5 different 4-dot rows, but using only 10 dots.  Rows must be straight.  Oh, and before you tricksters try giving me a single long string of dots, a 5-dot row does not count as 2 4-dot rows.  You can use a dot multiple times, but rows can't overlap.

Cubic Calendar

From http://www.folj.com/puzzles/

A corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month.

What numbers are on the faces of the cubes to allow this?

Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07".

A Lost and Hungry Vagabond

This is from the Car Talk Puzzler:
A lost and hungry vagabond happened upon a pair of travelers one of whom had three loaves of bread while the other had five. All of the loaves were the same size and weight.

The two travelers decided to share their bread with the vagabond, and that the eight loaves should be shared equally among the three of them. When they had finished, the vagabond reached into his pocket and pulled out eight coins. He handed three coins to the traveler who had had the three loaves and five to the other one and disappeared into the inky shadows.

The next morning, right after no breakfast, the one who had received the three coins said to the other one, 'I don't think he should have given three coins to me and five to you. It's not fair.' And he was right. How should the coins have been split up?

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)