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CTK Exchange
iliaden
Member since Aug-14-05
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Sep-17-06, 10:25 PM (EST) |
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"math championships"
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Hi, I am looking for ideas on where to look for any preparation for a math championship. I have already solved the problems of the previous years, yet they concern different topics.
Note: this question is concerning the Canadian Open Mathematics Challenge, thus the pre-university math, ending with calculus or linear algebra.
Thank you in advance Ilia |
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alexb
Charter Member
1924 posts |
Sep-22-06, 02:08 PM (EST) |
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1. "RE: math championships"
In response to message #0
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There is any number of books that may fit your short Description. There are several places that offer both olympiad books and training. Search for the publishers Art fo Problem Solving
MathProPress
American Mathematical Competitions
Mandelbrot Competitions Search for the authors Titu Andreescu
Paul Zeitz
Morrey Klamkin
Arthur Engel But there are really many more of both. |
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iliaden
Member since Aug-14-05
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Nov-28-06, 07:28 PM (EST) |
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3. "RE: math championships"
In response to message #0
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Thank you all for the suggestions. I already wrote the contest, yet there were a few questions for which I was unable to find an answer. this is (as it'seems to me) the hardest question: "What is the probability that if you throw a coin consecutively 10 times, you will have heads at least twice in a row?" I'm not asking the answer, but the way of solving it... HELP! |
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sfwc
Member since Jun-19-03
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Nov-29-06, 07:53 AM (EST) |
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4. "RE: math championships"
In response to message #3
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This problem is obviously closely related to that of determining the number of sequences of length n, in which each term is either H or T, and in which there are no two consecutive occurences of H. Call this number F(n). Obviously, given F(10), the problem may be solved. Try to find a simple formula with which you can work out F(n) from the values of F(i) with i < n. Since F(n) is easy to compute when n is very small, this solves the problem. Have fun, sfwc
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alexb
Charter Member
1924 posts |
Nov-29-06, 08:01 AM (EST) |
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5. "RE: math championships"
In response to message #3
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Consider relative probabilities assuming that there were M heads. If say Q(M) is the probability of having two successive heads in 10 throws, then Q(10) = Q(9) = Q(8) = Q(7) = Q(6) = 1
Q(5) = (C(10, 5) - 2) / C(10, 5)
...
Q(2) = (C(10, 2) - 9) / C(10, 2)
Q(1) = Q(0) = 0 Try thinking recursively to determine Q(3) and Q(4). |
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