Imagine you are the head of Human Resources at a large, successful high tech company. Your job depends on hiring the best and brightest minds in the world to produce new software and related products at an almost exponential pace. Your personal success depends on not only hiring better candidates than the competition, it must be accomplished within budget guidelines. You need employees who are “can’t miss” winners. Management has given you free reign to find these people. A reliable system must be in place to identify exceptional employees.
How are you going to proceed?
One way is through the use of puzzles. What? Puzzles? Since the early 2000s more and more companies, high tech companies initially and companies across the spectrum now , are using puzzle questions to identify future employees who can demonstrate critical thinking at the highest levels. Microsoft was one of the first large corporations to use puzzles to identify critical thinking skills. While that may be true but many smaller companies were already zeroing in on this method using logic-oriented questions which were one step away from puzzles. These tests were standardized; puzzle tests are not. The theory is if puzzles are constructed correctly, you will know all you need about the critical thinking abilities of the solver. Companies also utilize these types of questions to note the emotional responses of how candidates respond under pressure – intense focus required under strict time limitations. The other interesting aspect of this process is companies are dropping some of the usual criteria previously required for one to land a job. For the types of positions requiring large brains, they are not worried about social skills and from what college the applicant graduated. They want high-end thinkers. Period.
How did this evolve? The answer may be as easy as saying Bill Gates and the “Petals Around the Rose.” At one of the early computer conferences in 1977 Gates and Paul Allen, co – founders of Microsoft, were intrigued by the “ Petals ” game. A group of fellow computer attendees were headed home with Gates and Allen when they introduced the game to the pair. Gates was said to be so fascinated he would not leave the puzzle alone until he found the solution. Gates saw a whole new use for puzzles from this day forward. Want to see how you fare with the puzzle? A more detailed look at the puzzle can be found at http://www.borrett.id.au/computing/petals-bg.htm.
Now, many companies use puzzles for job applicants and it has proved to be a reliable identification process. It has become big enough business that author William Poundstone wrote a book titled How Would You Move Mount Fuji? Microsoft’s Cult of the Puzzle: How the World’s Smartest Companies Select the Most Creative Thinkers. (Little, Brown and Company, 2003). In this fun, informative book, Poundstone not only gives a history of this type of thinking behind the interviews but puzzles with possible solutions in the Answer Section. Notice I said “possible” answers. The reason for that is the puzzles used by companies seem to fall into two categories. One set of questions is more open-ended and allows for the candidates to discuss possible options and approaches for their solutions. Sometimes these questions seem impossible to answer.
Difficult Interview Brainteasers
Here are examples of these more “ open ended “ type questions found on numerous sites on the internet: 1) You are locked in an empty room with a working refrigerator as the only object in the room with you. The room is very warm and you are looking for a way to cool the room. What can you do? 2) What weighs more on the moon than on earth? How many garbage men are there in California? 3) And, of course, the book title question – How would you move Mount Fuji? (solutions are at the end of this article) These are not trivial. These are real questions and the blinking cursor is shining on the job applicants to unfurl their brilliance in front of people who might employ them and at a good salary.
The second group of questions are puzzles which separate the pretenders from the contenders. These are difficult, logic-based brainteasers with one answer and one answer only. No prior education or training is required, just the individual’s deductive/inductive reasoning abilities but under pressure. These are puzzles few people can answer and the process of solving them is just as important to the interviewer as the solutions. In other words, it might be okay to arrive at the wrong solution but if you processed the information in the right direction, it counts favorably. There are examples of these puzzles on the internet: actual puzzles that appeared on some of the interview tests. The problem with that is twofold. First, those puzzles are now removed from the interviewing process at all companies since the companies are quite aware the public has easy access to them. Secondly, the internet sites use the same handful of example puzzles again and again – so once you’ve solved them, you’ll need more. Practice, practice, practice. It’s no different than Peyton Manning working on his passing game for hours. The more puzzles you see and attempt, the better chance you have reaching their solutions. It also helps to gain confidence and become more relaxed in a testing environment.
For those interested in working on more difficult puzzles, there are some good resources. Several internet sites provide excellent material. Puzz.com has a broad spectrum of brainteasers of different varieties and at different levels. These are good “ warm – up “ puzzles. Macalester College has a math forum with archived puzzles and math problems which are world class (http://mathforum.org/wagon/). Nick’s Mathematical Games is an excellent resource (http://www.qbyte.org/puzzles/) as is Mathproblems.info with puzzles by Mike Shackleford (http://mathproblems.info/group1.html). Typing Difficult math brainteasers or or just plain Difficult Brainteasers into any of the search engines will provide some good sites.
There are additional resources and books listed at the end of this article.
To help the cause, I have created new brainteasers presented here for the first time. These are in line with the types you will encounter in an actual interview. No higher mathematics is required.
Stickels’ Original Brainteasers
Here are five puzzles for you to consider. I’ll give the answers with explanations at the end of the article. Try your luck at these to see if Bill Gates will be knocking on your door. Here’s a tip that may help. Approach these in the spirit of challenging fun and take the attitude that these puzzles are not bigger than you . . . or your mind. In other words, you want to be a “ mind ” warrior and conquer these. Do not accept defeat. You’ll need that type of attitude during an interview. Have fun.
You die and the devil says he’ll let you go to heaven if you beat him in a game. He sits you down at a round table. He divides a large pile of quarters in two so you both have the same amount of quarters in your own pile. He says, “Ok, we’ll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. The first guy who can’t put a quarter down loses. You cannot shift or try to squeeze any quarter into a space that moves another quarter.” The devil says he wants to go first.
You realize if the devil goes first, he probably has a strategy to win. You haven’t had time to think this through yet, so you ask for some time to consider your options. He grants you 15 minutes. At that end of that time you know how to beat him…but you also know you must go first for your strategy to win. You convince him to let you go first, saying you really didn’t have enough time to consider a strategy so you should at least go first. What is your winning strategy?
There’s an old puzzle that asks, “If a hen and a half lays an egg and a half in a day and a half, how many hens will it take to lay 6 eggs in 6 days? The answer is 1.5 hens. Here’s the new puzzle: at this rate, how many eggs will one hen lay in one day?
You are standing outside a 30-story building holding two identical glass spheres. You are told that either sphere, if dropped from the roof, would shatter upon hitting the earth, but that it would not necessarily break if dropped from the 1st story. Your task is to identify the lowest possible floor from which you can drop a ball and break it.
In the general case, what is the smallest number of drops required to guarantee that you have identified the lowest story? NOTES: 1) Both balls have the same minimum breakage story; 2) You only have two balls to use. If one breaks, it cannot be used for the rest of the experiment.
If the stack of cubes below was originally 5 x 5 x 5, is A, B, C, D or E the missing piece from the broken cube? Note: All rows and columns run to completion unless you actually see them end. The blocks seen in the five choices are to be placed back onto the cube upside down.
Using the numbers 5, 6, 7, and 8 once and only once, what is the largest number that can be created by “stacking” the numbers in exponential form?
You may stack the numbers any way you choose in any combination to achieve the largest number.
What is the second largest number?
Answers to “impossible” interview brain teasers:
1: The refrigerator puzzle
If you said open the door to cool the room, it wouldn’t be the best answer. In fact this will make the room even warmer by sucking the heat of the room into its cooling compartment and then pumping it through the coils on its back. A refrigerator is really a heat pump and it takes the heat away from the refrigerator and pumps it into the room. One good response would be to unplug the refrigerator and then open the door. It won’t result in a big cool down but it is the best you can do. This is a stretch but if you can move the refrigerator ( easily ) to a location in the room where the rising heat will move toward the vents higher on the wall, this will help a little.
2: The weight of an object on earth vs. moon puzzle
One of the keys here is to realize the earth has an atmosphere and the moon does not. That means that a balloon filled with helium would weigh nothing on earth but since there is no atmosphere on the moon, it would have a weight. Don’t get weight and mass confused here. The mass doesn’t change but the weight does. There is another aspect of this puzzle that might give the job candidate extra credit. If he or she said that the experiment would be impossible to do, you would probably be held in high regard. The reason is no inflatable balloon can exist in a vacuum and would explode immediately when introduced into that vacuum.
3: Garbage men in California
If you tried all kinds of mathematical or arithmetic gyration to come up with the answer, you are probably on the wrong track. One answer would be to call the state agency overseeing garbage collectors and ask them. Another good response is to call to ascertain if they are represented by unions. If so, call the union headquarters and ask them. Finally, if you are really quick on your feet and understand the importance of humor you might just give him or her a number. Remember, they are looking for an answer. Your position should be you are going to give them an answer. Give them a “ballpark” number and then say nothing more. If the interviewer asks how you arrived at your figure, your response should be (with a smile on your face), “When you hire me, I’ll tell you.” Human resource professionals love well-placed confidence.
4: How would you move Mount Fuji?
Read the book. I’m not going to take away Mr. Poundstone’s thunder.
Answers to the “five original puzzles”:
Put the first quarter exactly in the center of the (circular) table.
Next, for each quarter the opponent places, place one directly opposite it. That is, place it so that the center of the table is halfway between your piece and the opponent’s previous piece.
This will generate a completely symmetric layout of quarters on the table. This means that whenever the opponent selects a free space to place a quarter in, the space opposite is guaranteed to be free as well. Since you are always guaranteed an open space, you will never lose with this strategy.
The rate per hen per day is 2/3 egg. If a hen and a half lays an egg and a half in a day and a half, then one hen lays 1 egg in 1.5 days. 1.5 days is 3/2 days.
a) 1 hen X 3/2 days X rate per hen per day = 1 egg
b) 3/2 rate per hen per day = 1 egg
c) Multiply each side by 2/3…
Rate per hen per day = 2/3 egg
To test this, start from floor number 8 and drop a ball. If it doesn’t break then go to floor 15. If it doesn’t break there go to floor 21. If it doesn’t break there, go to floor 26. If it doesn’t break there, go to floor 30. If it doesn’t break there you have to test floors 27, 28, and 29. You have taken 8 drops to test this.
Now, take the other case: suppose you drop one ball on floor 8 and it breaks. You now have to test floors 1 through 7 to find out if that ball will break. That, also, totals 8 as does each testing stage between any of the two consecutive floors you’ve chosen. Notice how the difference between each set of consecutive floors decreases by 1…8, 15, 21, 26 and 30? An easy way to find the minimum number of drops for any floor is to add 1+ 2 + 3 + 4 +…until the sum reaches the number of the top floor. As I demonstrated in the first sentence, once the number has been met (even if the last added number surpasses the top floor number when adding it, it is taken to that whole number to determine the minimum number of attempts) that is the solution: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 so the threshold of 30 has been passed after the 8 is added. Therefore, it takes a minimum of 8 drops.
Figure D is the missing piece from the broken cube.
The largest number is approximately 10 to the 4.5 millionth power. It is the largest number by a long way.
William Poundstone is the author of over 11 books. A few of his most popular are Carl Sagen: ALlife in the Cosmos ( Henry Holt Publishing, 1999 ) . Prisoner’s Dilemma, John von Neumann, Game Theory, and the Puzzle of the Bomb ( Doubleday Publishing, 1992 ) Labyrinths of Reason, Paradox, Puzzles, and the Fraility of Reason ( Doubleday Publishing, 1988 ) and Big Secrets, The Uncensored Truth About All Sorts of Stuff You Are Never Supposed to Know). He has written for Esquire, Harper’s, the Economist and has been nominated twice for the Pulitzer Prize.
John Kador’s HOW TO ACE THE BRAIN TEASER INTERVIEW ( by McGraw – Hill, 2004 )
ADVANCED APTITUDE TESTS by Jim Barrett and HOW TO PASS ADVANCED APTITUDE TESTS by Jim Barrett (both by Kogan Page Publishing. The first was published in 2004. The second was published in 2002)
THE POWER OF LOGICAL THINKING: EASY LESSONS IN THE ART OF REASONING . . . AND HARD FACTS ABOUT ITS ABSENCE IN OUR LIVES by Marilyn vos Savant, published by St. Martin’s Griffin, 1997
BRAIN BUILDING IN JUST 12 WEEKS by Marilyn vos Savant and Leonore Fleischer, published by Bantam Books, 1990
Two books not specifically designed for interviews but can be used for mental warm ups for sharpening spatial/visual skills –
OFFICER CANDIDATE SCHOOL TESTS by Rod Powers ( Barron’s Educational Series, Inc. 2006)
MECHANICAL APTITUDE and SPATIAL RELATIONS TESTS, 4 th Edition, ( ARCO Publishing, 1999
Two books by Martin Gardner – Aha! Insight published by Scientific American, 1978 and Aha! Gotcha, published by W.H. Freeman, 1982 ( originally Scientific American, Inc. 1975)
The Great Book of Mind Teasers & Mind Puzzlers by George J. Summers, published by Sterling Publishing. (The Great Book of Mind Teasers & Mind Puzzlers is a combined edition of Mind Teasers, 1977, and Mind Puzzlers, 1984, both published by Sterling Publishing and both written by George J. Summers ).
Dover Publications has a catalog of some of the older puzzle books that can be viewed and ordered at www.doverpublications.com. Many of these puzzle books offer excellent brainteasers.