During an interview for a position to code at a software company, a candidate is typically asked to code in real time an assigned problem or to mentally solve puzzles in logic. The first company I’m aware of that adopted this practice was Microsoft at its founding. In this spirit, we continue our series of Micro Softy puzzles — questions that might have been asked in such an interview. 

We’ll give the answer to last week’s puzzle (what happened to the extra dollar?) after presenting a new classic puzzle in simple graph theory:

Shown below is an image of a three-by-three array of dots. There are two parts to this puzzle:

• First connect all nine dots with no more than four perfectly straight lines. The lines must be connected. In other words, the four lines must be drawn without picking your pencil off the paper.
• The second part of the puzzle is to identify what commonly used phrase resulted from the solution to this puzzle?

We’ll give the answers to both parts next week.

And now, here’s the answer to Micro Softy 11 from last Monday:

What Happened to That Other Dollar?

Here is the problem: David is a boy band with five members, all named David. Their groupies, Shirley, Goodness, and Mercy, follow them on tour to Toad Suck, Arkansas, where they find a $10-per-room hotel. After they have paid $30 for three rooms, the clerk realizes there’s a $25 discount and sends Uriah, the bellhop, to return $5. Greedy Uriah pockets $2 and gives each groupie $1. The group ends up paying $27 in total ($9 each), and Uriah keeps the other two dollars. $27 + $2 = $29. The question arises: where’s the missing dollar?

Answer: There is, of course, no missing dollar. There is only failed logic and a seductively misleading description of where the money went. To see this, make a list of where the money ended up.

            $25 … paid for the rooms

            $ 2 … in Uriah’s pocket

            $ 3 … returned to the girls

There’s no missing dollar. The $27 paid by Shirley, Goodness, and Mercy includes the $25 for the rooms and the $2 kept by Uriah. Adding Uriah’s $2 to the $27 is a misdirection, as it doesn’t align with the actual distribution of the money. The $2 kept by Uriah was part of the money paid by the girls. To the $27 paid by the girls should be added the $3 returned to them. That gives the right answer and it doesn’t violate the law of conservation of money.

Note: At Monday Micro Softy 11:  What Happened to That Other Dollar?, you will also find links to the first ten Micro Softies. Have fun!

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Footnote: It’s time for a disclaimer reminder. The Micro Softies in this ongoing column have been gathered over many years, and I’ve since lost track of their exact origins. There is no claim to originality. Some general sources include oral anecdotes from students interviewed by Microsoft for coding jobs, the column “Mathematical Games” by the late Martin Gardner in Scientific American, the Puzzler section of Car Talk on PBS Radio, Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine, and the book Introduction to Evolutionary Informatics.

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