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Topic: More University Interview Questions (Read 661 times) |
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ThudnBlunder
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More University Interview Questions
« on: Jan 19th, 2005, 12:13am » |
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Three brilliant students go for separate interviews with a university admissions officer, a number theorist. He chooses 4 whole numbers and tells the 1st student their product. The student tells him the 4 numbers. He tells the 2nd student the sum of the squares of the 4 numbers and she duly tells him the 4 numbers. 'Too easy', he thinks. So he tells the 3rd student the sum of the 4 numbers. The student was unable to tell him the 4 numbers.
What 4 numbers did he choose?
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| « Last Edit: Jan 19th, 2005, 12:14am by ThudnBlunder » |
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Grimbal
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Re: More University Interview Questions
« Reply #1 on: Jan 19th, 2005, 4:09am » |
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:: 1, 1, 1, 3 :: ?
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Eigenray
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Re: More University Interview Questions
« Reply #2 on: Jan 19th, 2005, 5:59am » |
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What is a whole number?
The first student must have known none of the numbers were negative. And we know there were no 0s, but do the second and third students know that?
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| « Last Edit: Jan 19th, 2005, 6:00am by Eigenray » |
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ThudnBlunder
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Re: More University Interview Questions
« Reply #3 on: Jan 19th, 2005, 11:41am » |
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on Jan 19th, 2005, 5:59am, Eigenray wrote:What is a whole number?
The first student must have known none of the numbers were negative. And we know there were no 0s, but do the second and third students know that? |
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Although Bourbaki includes zero in the set of whole numbers, I believe for the purpose of this puzzle we should use A000027
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Icarus
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Re: More University Interview Questions
« Reply #4 on: Jan 19th, 2005, 7:45pm » |
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Bourbaki is not the only one. Traditionally,
The Natural numbers = 1, 2, 3, 4, ...
(The name comes from the Greeks, who considered other numbers as being contrived. They were not aware of the concept of 0, so 0 is not included).
The Whole numbers = 0, 1, 2, 3, 4, ...
(Since the Naturals did not include 0, when the concept of 0 was introduced into western mathematics, a new name was needed for the set with 0.)
Considering the Whole numbers to be 1, 2, 3, ... is rather ridiculous, as we already have a perfectly good name for those numbers.
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Eigenray
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Re: More University Interview Questions
« Reply #5 on: Jan 19th, 2005, 9:59pm » |
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Most logicians I know (and certainly many others) consider 0 a natural number -- it's the equivalence class of a finite set, viz, {}.
[bbn]={{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},...} 
Waclaw Sierpinski, the great Polish mathematician... was worried that he'd lost one piece of his luggage. "No, dear!" said his wife. "All six pieces are here." "That can't be true," said Sierpinski, "I've counted them several times: zero, one, two, three, four, five."
--- The Book of Numbers, John Conway and Richard Guy
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| « Last Edit: Jan 19th, 2005, 10:20pm by Eigenray » |
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Icarus
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Re: More University Interview Questions
« Reply #6 on: Jan 20th, 2005, 3:40pm » |
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It is becoming common to include 0 in the Naturals, but this is a fairly recent change. Traditionally, it was not.
And since the Naturals are being redefined to be the Wholes, I suppose it is not surprising that Wholes are being redefined to be the naturals.
However, we can settle the entire thing by saying that the professor chose 4 "positive integers". (And no, zero is not positive!  )
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