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On a geography test you have to tell which of two German cities is greater in population for all possible pairs of the 80 largest cities of Germany. (And that’s the only task on the test since it’s already 5 pages long.) But you didn’t study last night, and only even recognise half the cities, and don’t even know how those are ordered relative to each other. Your friend on the other hand studied dutifully all night and recognises all the cities and even knows how two cities are ranked relative to each other 60% of the time.
A week later you get the testresult and you have a higher score than your friend. How come?
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There are three Federation Officers assigned to take three hostile aliens to “Peace Talks” on another planet. However, they must follow the following rules:
They have only one small space ship.
Only two individuals can ride in the space ship each time.
All Federation Officers can pilot the space ship, but only one alien can pilot the ship.
If at any time there are both Federation Officers and aliens on a planet, then there must always be more (or the same number of) Federation Officers than aliens on that planet. This is because if there are more aliens than Federation Officers, then the aliens will kill the Federation Officers. Count any individual in the space ship when it is on one planet as being on that planet.
The one space ship is the only means of transportation. There is no other way to get to the “Peace Talks”. No one can exit the space ship while it is in flight.
To start off, all the Federation Officers and aliens are on the same planet.Can all Federation Officers and aliens get to the other planet alive, and if so: how?
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A stopped clock gives the exact time twice a day, while a normally running (but out of sync) clock will not be right more than once over a period of months. A clever grandfather [as in grandfather clock] adjusted his clock to give the correct time at least twice a day, while running at the normal rate. Assuming he was not able to set it perfectly, how did he do it?
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Jenny has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes, she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes, she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.
The question: How many boxes has Jenny used in total?
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You are given “n” coins of denominations 1, 0.5, 0.25, 0.1, 0.05 and 0.01 (6n coins altogether). You are then asked to choose n out of these 6n coins that sum up to exactly 1. What is the smallest n for which this is impossible?
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Assume that you have a number of long fuses, of which you only know that they burn for exactly one hour after you lighted them at one end. However, you do not know whether they burn with constant speed, so the first half of the fuse can be burnt in only ten minutes while the rest takes the other fifty minutes to burn completely. Also, assume that you have a lighter.
How can you measure exactly three quarters of an hour with these fuses?
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A confused bank teller transposed the dollars and cents when he cashed a cheque for Ms Denial, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Denial noticed that she had left exactly three times as much as the original cheque. What was the amount of the cheque ?
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