# Solve the Equation, Get an Interview

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.

### Web Extra Puzzles

**Problem 2:** You've got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day.

If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

**Problem 3:** Imagine a disk spinning like a record player turntable. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors.

How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?

**Problem 4:** There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side.

It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.

Woman 1: 1 minute to cross

Woman 2: 2 minutes to cross

Woman 3: 5 minutes to cross

Woman 4: 10 minutes to cross

For example, if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission.

What is the order required to get all women across in 17 minutes?