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The eyes of most candidates completely glaze over as soon as they are presented with this puzzle The first thing to do is relax With a puzzle like this, there s always a trick or shortcut No interviewer wants to stump you or watch you actually calculate this value The interviewer wants to see how you react to a seemingly unmanageable puzzle Do you panic and give up Do you start working Or do you start thinking
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What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1,000
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Hint: Work backwards This puzzle looks much more difficult than it is The first thing is to look for a clue That nice round final number of 1,000 is the place to start Look for a series that reduces the value to another nice round number either that or a zero along the way that reduces the eventual value to zero But in this case, it s a series that actually solves for a nice round number One good tactic for puzzles of this sort is to work backward If you do, the problem becomes manageable Working backward, 9/10 of 1,000 is 900; 8/9 of 900 is 800; 7/8 of 800 is 700; 6/7 of 700 is 600; 5/6 of 600 is 500; 4/5 of 500 is 400; 3/4 of 400 is 300; 2/3 of 300 is 200; and 1/2 of 200 is 100 Solution: 100
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Many puzzles posed in job interviews feature probability-related themes This should not be surprising Many, perhaps most, business decisions have a critical element of probability at their core Should we introduce a new product What are the chances of its success What is the likelihood our competitor will match us What s the likelihood our medicine will win FDA approval All these puzzles call on formal or informal understanding of such concepts as permutation, combination, sample spaces, and dependent and independent events An understanding of these concepts and the ability to apply them to problems is an essential business skill
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On one level, this is a simple arithmetic problem with a hint of probability tossed in But the puzzle tests understanding of outcomes in an interesting way
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Assume you are blindfolded and placed in front of a large bowl containing currency in $50, $20, $10, and $5 denominations You are allowed to reach in and remove bills, one bill at a time The drawing stops as soon as you have selected four-of-a-kind four bills of the same denomination What is the maximum sum of money you could accumulate before the drawing ends
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Hint: Resist overconfidence The interviewer expects you to think Many candidates guess, incorrectly, that the answer is $170 three $50 bills plus a $20 bill But that misses the possibility that 12 bills could be
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drawn before picking four bills of the same denomination The maximum value that can be picked is $305 three $50s, three $20s, three $10s, three $5s, and the last bill, that ends the selection, would be another $50 bill Solution: $305
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This is a nice probability puzzle, not overly difficult but with a little edge It requires the candidate to listen especially closely to the precise wording of the puzzle As a general rule, it is always critical to listen to the precise wording of the challenge
A gambler is holding three coins One coin is an ordinary quarter, the second has two heads, the third has two tails The gambler chooses one of the coins at random and flips it, showing heads What is the likelihood that the other side is tails
Hint: The challenge is not to calculate the probability of tails coming up Think this one through How many heads and tails do these three coins represent Three and three, respectively It s tempting then, to conclude that there s a 50 percent chance of showing tails But listen to the instructions The gambler s first toss shows heads The challenge is to calculate the probability that the other side of this coin shows tails Since only one of the three coins has tails opposite, the answer is one out of three Solution: One-third
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