Category: puzzles

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When I was a kid, my father introduced me to the New York Times Crossword Puzzle. Dad commuted from our house to New York City every weekday, and often rode the Long Island RailRoad. He took the puzzle every day. He solved it in pen. He also solved the cryptograms in pen. I was impressed.

He taught me some basic logic for the solution of both puzzles. I did the cryptograms for awhile, but didn’t get into the crossword puzzle until a few years ago. My wife and I try to do it every Thursday through Sunday.

You may not know this (I didn’t, until my dad tipped me off a few years ago)….

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Original Photo by Norsehorse Edited by Brian

Ah, I love it when readers beat me to the punch!

The comments to the original post pretty much sum up the paradox and it’s solution very well.

Khaled’s and Mark’s comments illustrate perfectly one of the things I wanted to point out about this puzzle. That point is:

Just because something is phrased a certain way is not reason to assume that that phrasing is the best way to represent the problem. And one way to critically examine the situation is to reframe it in a mathematical equation.

Khaled said, “Interesting how, once you assume that you can implicitly trust a given source, you can be led through any logic, or illogic, and have a lot of trouble pulling yourself back to a critical mindset.”

How true. Then Mark gave a good method to understand how to see where the paradox lies when he said, “I started to write an equation, because properly written equations can solve all counting problems, but then realized that this was pointless, because adding 2 dollars to the 27 dollars the guests paid did not reflect what happened.”

Exactly! The question was phrased to lead you to believe that because the facts were a certain way (which it accurately represented) you had to see it in a certain way (which was anything but accurate).

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Original Photo by Norsehorse Edited by Brian

There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this:

Three men go into a motel. The man behind the desk said that the room costs $30. So each man paid $10 and went to the room.

Later, the desk clerk realized that the room was only $25. So he sent the bellboy to the men’s rooms with five one-dollar bills.

The bellboy couldn’t figure out how to split five dollars evenly three ways, so he gave each man one dollar, and kept the other two for himself.

This meant that the three men had each paid $9 for their rooms, which makes a total of $27 dollars. Adding the two dollars that the bellboy kept would make a total of $29 dollars.

So where is the other dollar?

My advice to anyone trying to solve anything like this, or trying to think about anything at all, for that matter, is not to jump to conclusions.

Want to give it a try and add your thoughts in a comment? Go for it! I’m not asking for the solution, just some thoughts about the meaning of the puzzle - how it relates to life, logic, decision-making and understanding your world. I am not putting this up as a trivial puzzle.

My comments will be in the next post.

(Note: When I originally posted this, there were a few typos and other mistakes in it. If you busted your head over it till now, please accept my apologies. It should be correct now.)

This post is concerned with a very interesting problem, called “The Traveler’s Dilemma.” There is a very good article about it, written by it’s creator, Professor Kaushik Basu, in the June, 2007 issue of the Scientific American. The article begins:

“When playing this simple game, people consistently reject the rational choice. In fact, by acting illogically, they end up reaping a larger reward–an outcome that demands a new kind of formal reasoning.”

Please read the article before you read this post.

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Today I received an e-mail from an astute reader, regarding the Question of the Week for the fourth week of March, 2003. The question was:

Which is worth more, a pound of $5 gold coins, or a pound of $10 gold coins? Explain why.

Before I go into the reader’s observations, let me tell you the answer:

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