শব্দ সংখ্যা
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
নীরব এবং সেতু পরস্পরের সাথে কথা বলার জন্য এক ধরনের ভাষা ব্যবহার করছে। এই ভাষায় 5 টা বর্ণ ব্যবহৃত হয়- a,b,c,d এবং e। এই ভাষার প্রত্যেকটি শব্দে এই 5 টি বর্ণ থাকবেই। এই 5 টি বর্ণ নিয়ে গঠিত ঐসব শব্দই এই ভাষার অন্তর্ভুক্ত যেসব শব্দে বর্ণগুলো তাদের alphabetic ক্রমে নেই। যেমন: adbec এই ভাষার শব্দ না কারণ a তার alphabetic ক্রমে রয়েছে। আবার eabcd এই ভাষার একটি শব্দ কারণ এদের একটি বর্ণও alphbetic ক্রমে নেই। তাহলে এই ভাষায় কয়টা শব্দ আছে?
- nafistiham
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Re: শব্দ সংখ্যা
derangement of $5=44$
(got it from a book.but don't know the way to find a derangement )
(got it from a book.but don't know the way to find a derangement )
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: শব্দ সংখ্যা
my ans is also 44.i used PIE to figure out the number of words where some letters are in their alphabetic order.
Re: শব্দ সংখ্যা
I also didn't get that 'Derangement' thing....
can anyone explain?
can anyone explain?
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- nafistiham
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Re: শব্দ সংখ্যা
see the definition from the book Daniel A. Marcus - Combinatorics (A Problem Oriented Approach) - MAA, 1998 page 8
actually it is the special rearrangement of a string such that no element is in its original position.
actually it is the special rearrangement of a string such that no element is in its original position.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: শব্দ সংখ্যা
আচ্ছা, এখানে তো বলা হয় নাই যে, শব্দে ৫টার বেশি বর্ণ থাকতে পারে না। তাহলে তো শব্দ সংখ্যা অসীম হবে(একটা বর্ণ তো একাধিক বারও ব্যবহৃত হতে পারে, তাই না)।
অম্লান সাহা
Re: শব্দ সংখ্যা
তিহাম, আমি এত বোকাও নারে ভাই... :p
ঐটা বুঝসি... কিন্তু প্রমান্টা বুঝতে পারতেসি না!!
ঐটা বুঝসি... কিন্তু প্রমান্টা বুঝতে পারতেসি না!!
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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- nafistiham
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Re: শব্দ সংখ্যা
sorry, labib vy.
but,here is nothing to prove i think.because, the q says to find the number of arrangements that has no letter in its alphabetic position.the meaning i get is $a,b,c,d,e$ cant be in $1^{st},2^{nd},3^{rd},4^{th},5^{th}$ positions.so,the derangement should be the answer.
amlan da,if the q would be thus, i don't think there could be a definite solution.because, by adding any of the letter we can change there position.and, like you said the number would be infinity
but,here is nothing to prove i think.because, the q says to find the number of arrangements that has no letter in its alphabetic position.the meaning i get is $a,b,c,d,e$ cant be in $1^{st},2^{nd},3^{rd},4^{th},5^{th}$ positions.so,the derangement should be the answer.
amlan da,if the q would be thus, i don't think there could be a definite solution.because, by adding any of the letter we can change there position.and, like you said the number would be infinity
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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Re: শব্দ সংখ্যা
তিহাম, সেটাই তো বলছি। এটার কোন নির্দিষ্ট উত্তর নাই। মানে শব্দ সংখ্যা অসীম।
অম্লান সাহা
Re: শব্দ সংখ্যা
অম্লান দা, কথা সত্যি কিন্তু আমার মনে হয় আমরা সবাই জানি... এইখানে কি চাইসে...
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes