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Solve the Equation, Get an Interview

One of the Google recruiting billboards that featured a complex math problem.
One of the Google recruiting billboards that featured a complex math problem.

Stanford mathematician Keith Devlin talks with NPR's Scott Simon about the idea of using logic and quantitative reasoning puzzles to screen job applicants in the high-tech industry. Long a niche recruiting tactic, the method was popularized by Microsoft in the 1990s.

The Web search engine company Google recently made a very public display of its attempt to attract math whizzes. It launched a billboard advertising campaign featuring a complex equation in front of the domain root ".com" — making the puzzle's solution a Web address. Candidates who made it to that page were asked to solve a harder second problem, which in turn guided them to yet another Web page that asked for their resume.

The actual value of using puzzle questions to find employees is heavily disputed, even for positions in computer programming and engineering. It has been reported that even Microsoft makes less use of such questions than it has in the past.

Devlin's Job Interview Puzzle

Problem 1: Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?

Answer: After 12 o'clock, the minute hand races ahead of the hour hand. By the time the minute hand has gone all the way round the clock and is back at 12, one hour later (i.e., at 1 o'clock), the hour hand has moved to indicate 1. Five minutes later, the minute hand reaches 1 and is almost on top of the hour hand, but not quite, since by then the hour hand has moved ahead a tiny amount more. So the next time after 12 that the minute hand is directly over the hour hand is a bit after 1:05. Similarly, the next time it happens is a bit after 2:10. Then a bit after 3:15, and so on. The eleventh time this happens, a bit after 11:55, has to be 12 o'clock again, since we know what the clock looks like at that time. So the two hands are superimposed exactly 12 times in each 12 hour period.

To answer the second part of the puzzle, you have to figure out those little bits of timer you have to keep adding on. Well, after 12 o'clock there are eleven occasions when the two hands match up, and since the clock hands move at constant speeds, those 11 events are spread equally apart around the clock face, so they are 1/11th of an hour apart. That's 5.454545 minutes apart, so the little bit you keep adding is in fact 0.454545 minutes. The precise times of the superpositions are, in hours, 1 + 1/11, 2 + 2/11, 3+ 3/11, all the way up to 11 + 11/11, which is 12 o'clock again.

Want more? Devlin has provided three additional puzzles in the right-hand column of this page. If you think you know answers to any of these problems, send your replies to wesat@npr.org.

Copyright 2022 NPR. To see more, visit https://www.npr.org.

Scott Simon is one of America's most admired writers and broadcasters. He is the host of Weekend Edition Saturday and is one of the hosts of NPR's morning news podcast Up First. He has reported from all fifty states, five continents, and ten wars, from El Salvador to Sarajevo to Afghanistan and Iraq. His books have chronicled character and characters, in war and peace, sports and art, tragedy and comedy.
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