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Topic: Teacher, Students and Five Functions Puzzle (Read 811 times) |
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K Sengupta
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Teacher, Students and Five Functions Puzzle
« on: Dec 1st, 2009, 8:30am » |
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A mathematics teacher chose three students to conduct an experiment. He said, "I have chosen a 3-digit positive decimal integer N, with the first digit not more than the second, and the second not more than the third. I have also chosen a function F(N), which is one of the following functions:
(i) SUM (N) = the sum of the digits of N.
(ii) PROD (N) = the product of the digits of N.
(iii) SSQ(N) = the sum of the squares of the digits of N.
(iv) SSC(N) = the sum of the cubes of the digits of N.
(v) LCM(N) = the least common multiple of the digits of N.
"I then calculated the value V=F(N) , and have written the three items N, F and V, each on a separate piece of paper and will give one to each of you. You must try to determine the other 2 items. You may use your computers, but cannot collaborate. This is not a competition, only an experiment. Just make your lists, and we will see what happens."
Here is what happened:
1:00 – Students begin working
1:20 - Teacher asks if anyone had the answers. No one had.
1:30 - Teacher asks if anyone had the answers. No one had
1:31 - Teacher asks if it would help them if he told them whether N was odd or even. All three say no.
1:40 - Teacher asks if anyone had the answers. No one had
1:41 - Teacher asks if it would help them if he told them whether V was odd or even. All three say no.
1:50 - Teacher asks if anyone had the answers. No one had.
1:51 - Teacher asks if it would help them if he told the sum of N and V. All three say no.
2:00 - Teacher asks if anyone had the answers. All three had.
What were the three items?
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| « Last Edit: Dec 1st, 2009, 8:31am by K Sengupta » |
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pex
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Re: Teacher, Students and Five Functions Puzzle
« Reply #1 on: Dec 1st, 2009, 9:29am » |
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Looks like 32 + 32 + 62.
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Hippo
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Re: Teacher, Students and Five Functions Puzzle
« Reply #2 on: Dec 1st, 2009, 3:12pm » |
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I don't understand the riddle. Why would the teacher ask for what he knows?
Probably better formulation would be ... at time t teacher informed them none of yours can know the answer now.
... at time ... knowing ... parity of ... would not help anybody of yours ...
... now the exam ends, let me take your written answers ...
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towr
wu::riddles Moderator
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Re: Teacher, Students and Five Functions Puzzle
« Reply #3 on: Dec 2nd, 2009, 1:19am » |
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on Dec 1st, 2009, 3:12pm, Hippo wrote:| I don't understand the riddle. Why would the teacher ask for what he knows? |
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He asks them for what they know, at the given moments.
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Wikipedia, Google, Mathworld, Integer sequence DB
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nks
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Re: Teacher, Students and Five Functions Puzzle
« Reply #4 on: Dec 2nd, 2009, 4:17am » |
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I think the solution will go in this direction. It is in question.
First step : All have to find the whether N is odd or even.
once it is known then in second step
All have to find whether V was odd or even, Becoz it depend upon N.
Now N and V are known then , All have to try to find sum of N and V it means They know the value of N and V,
Finally function can be found via N and V.
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Hippo
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Re: Teacher, Students and Five Functions Puzzle
« Reply #5 on: Dec 2nd, 2009, 5:57am » |
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on Dec 2nd, 2009, 1:19am, towr wrote:
He asks them for what they know, at the given moments. |
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But he knows what they should know. And we must suppose they are smart enough...
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pex
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Re: Teacher, Students and Five Functions Puzzle
« Reply #6 on: Dec 2nd, 2009, 7:03am » |
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on Dec 2nd, 2009, 5:57am, Hippo wrote:| But he knows what they should know. And we must suppose they are smart enough... |
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So, teachers should never use exams?
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Hippo
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Re: Teacher, Students and Five Functions Puzzle
« Reply #7 on: Dec 2nd, 2009, 1:31pm » |
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on Dec 2nd, 2009, 7:03am, pex wrote:
So, teachers should never use exams? |
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By asking questions whose answers he knows and students cannot deduce?
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