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I was having coffee at Starbucks with my nephew Kartik the other day. He looked up at the door and a grin lit up his face. A woman, about his age, was walking in. He stood up, completely ignoring the fact that I was in the middle of a sentence, and was at her side in a bound.
They met like old friends (from their college days, it turns out, where they sat next to each other in Math and Logic classes) and after they had declaimed loudly about how l-o-n-g it was since they had last met, and had exchanged Facebook IDs, he asked her the inevitable question:
So, I ask you! [To solve this problem, you will probably need paper and something to write with.] |
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The mathematics professor in the city college lives on the odd-numbered side of a street. The first house is numbered "1"
and each house is 2 more than the previous one. There are no gaps in the addresses.
When he comes home at the end of a busy day, he gets off the bus right in front of house #1. Since his mind is full of mathematical conundrums, he finds it hard to remember the number of his own house. Instead, as he walks by each house, he adds its address to the ones before. When the total reaches a certain number that he has memorized, he stops, takes out the keys from his pocket, opens the door and enters his house. One day, even more absent-minded than usual, he gets off the bus on the high-numbered end of the street. As usual, he adds up house numbers (starting from, as we know, the highest-numbered house on his street). When the total reaches the number that he has memorized, he stops, takes out the keys from his pocket, opens the door and enters his house. Given that his house number is in two digits, what is it? [To solve this problem, you could use a tool like Excel. But you cannot use more than three columns or more than 50 rows for your solution.] |
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In an effort to gauge the perspicacity of their staff, management of a well-known international organization calls a
meeting and warns the 38 staff of an upcoming test.
"Tomorrow morning at 10am," the management speaker says, "you will all gather in the corridor on the 11th floor. You will be asked to stand in single file so that each individual can see all the people standing in front of them and none behind. From a large closed box containing an unknown number of blue and yellow hats, I will place one hat on each person's head. When I have finished, you will each have one (and only one) turn. Starting at the back of the line, you will say one word – ‘blue’ or ‘yellow’. You cannot use inflection, tonality or other signal -- like a cough -- to impart information in addition to that word. Those who cannot correctly say the color of their hat should leave their identity card in the bin when they leave work at the end of the day. If anyone willingly disobeys the rules, the whole lot of you will be thrown out the window on to the street below where marauding panhandlers will trample you to dust." So now, the 38 staff have a day to come up with a plan. They have worked well together these past few months and they are loathe to part with their colleagues. They know that they can all correctly tell blue from yellow -- none of them has a language problem or is colorblind. What plan does the team come up with to keep the team as intact as possible? What is the greatest risk they manage to limit themselves to? |