Critical Section

the $21 question

Thursday,  05/29/03  11:34 AM

A few days ago I reviewed How Would You Move Mount Fuji, a great new book about the logic puzzles often used in technical interviews.  I received a lot of feedback - thanks! - and some interesting meta-reviews (reviews of my review).  My favorite meta-review was by Chris Lightfoot.  He was pretty critical - as he put it "such pontifications irk me" - but the reason I liked it was that he gave a different and better answer to the $21 question.

You may remember this question goes as follows:

Mike and Todd have $21 between them.  Mike has $20 more than Todd.  How much does each have (you can't use fractions in the answer)?

I called this the worst question in the book, based on the fact that it has no answer.  I went on to say:

Apparently sometimes people ask questions which have no answer to see how candidates react.  This might be helpful in some situations (if you're hiring for a company with a confrontational culture!), but I would never use it; I don't like what it says about me and my company, and I can't imagine what it would say about the candidate, either.

So it turns out that this question does have an answer!  Chris writes:

What does this illustrate?  That Ole apparently doesn't know that dollars are divided up into cents:

m = t + 2000¢
m + t = 2100¢


m = 2050¢
t = 50¢

Excellent!  When I read this question in the book it was described as having no answer, and it never occurred to me that the book was wrong, and that this question really does have an answer.  I believe whoever first posed this question was looking for Chris' answer; this is a classic "thinking out of the box" test.  Any candidate is going to do the algebra and conclude that there is no integer solution in dollars.  Will they then consider shifting units to cents?  Very interesting.

I don't know what my reaction would have been if the question had been posed as answerable.  Would I have thought to give the answer in cents?  Don't know.  But when the book stated that the question was not answerable, I took their word for it.  Bad Ole.

Since I'm following up on the review, I wanted to mention a couple of other puzzles which were emailed to me as great questions:

The Bad King.  I had encountered some version of this before, and I like it.  I knew the form of the answer from having seen it before.  This question does have an answer and there is no trick - just logical thinking.  Click through if you want to try it.

The Switches Puzzle.  I have not figured this one out yet - it seems like it requires a trick, but according to the techInterview rating scheme the "aha" factor is low, implying that it doesn't.  Check it out if you're interested - if I can figure it out, I'll post a solution.

[ Later - I figured it out!  Please see The Two Switches for the solution. ]

In the meantime let me know if you encounter other interesting puzzles...  I'm practicing for the Worlds :)

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