BdMO National Junior 2020 P4

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Mursalin
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BdMO National Junior 2020 P4

Unread post by Mursalin » Thu Feb 04, 2021 12:20 am

একটি সুডোকু টুর্নামেন্টে এ র‍্যাংকিং এর শীর্ষে থাকা \(10\) জন প্লে-অফ ম্যাচ খেলে। র‍্যাংকিংয়ের #\(10\)-এ থাকা অংশগ্রহণকারী #\(9\)-কে চ্যালেঞ্জ করে এবং যে হারে সে \(10\)th প্রাইজ পায়, আর যে জিতে সে র‍্যাংকিংয়ের #\(8\)-কে চ্যালেঞ্জ করে। এদের মধ্যে যে জিতে সে আবার #\(7\)-কে চ্যালেঞ্জ করে এবং যে হারে, সে \(9\)th প্রাইজ পায়। এভাবে সবশেষে কেউ #\(1\) কে চ্যালেঞ্জ করে, আর সে খেলায় যে জিতে, সে \(1\)st প্রাইজ পায়। এই সুডোকু প্লে-অফে অংশগ্রহণকারীরা মোট কতভাবে প্রাইজ পেতে পারে?

In a sudoku-tournament, the winner will be selected from play-offs among the top \(10\) ranked participants. The participants at #\(10\) and #\(9\) of the ranking will challenge each other, the loser will receive \(10\)th prize and the winner will challenge #\(8\). The winner of the first challenge and #\(8\), will challenge #\(7\) and the loser will receive \(9\)th prize. The ultimate winner will be the one who receives the \(1\)st prize. In how many ways these \(10\) participants may receive the prizes?
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Anindya Biswas
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Re: BdMO National Junior 2020 P4

Unread post by Anindya Biswas » Sun Feb 07, 2021 12:37 am

Mursalin wrote:
Thu Feb 04, 2021 12:20 am
একটি সুডোকু টুর্নামেন্টে এ র‍্যাংকিং এর শীর্ষে থাকা \(10\) জন প্লে-অফ ম্যাচ খেলে। র‍্যাংকিংয়ের #\(10\)-এ থাকা অংশগ্রহণকারী #\(9\)-কে চ্যালেঞ্জ করে এবং যে হারে সে \(10\)th প্রাইজ পায়, আর যে জিতে সে র‍্যাংকিংয়ের #\(8\)-কে চ্যালেঞ্জ করে। এদের মধ্যে যে জিতে সে আবার #\(7\)-কে চ্যালেঞ্জ করে এবং যে হারে, সে \(9\)th প্রাইজ পায়। এভাবে সবশেষে কেউ #\(1\) কে চ্যালেঞ্জ করে, আর সে খেলায় যে জিতে, সে \(1\)st প্রাইজ পায়। এই সুডোকু প্লে-অফে অংশগ্রহণকারীরা মোট কতভাবে প্রাইজ পেতে পারে?

In a sudoku-tournament, the winner will be selected from play-offs among the top \(10\) ranked participants. The participants at #\(10\) and #\(9\) of the ranking will challenge each other, the loser will receive \(10\)th prize and the winner will challenge #\(8\). The winner of the first challenge and #\(8\), will challenge #\(7\) and the loser will receive \(9\)th prize. The ultimate winner will be the one who receives the \(1\)st prize. In how many ways these \(10\) participants may receive the prizes?
It's not fully clear to me what does a way means for receiving the prize is. When should we consider them different? Can anyone clarify this question for me? :)
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
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Pratik12345
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Re: BdMO National Junior 2020 P4

Unread post by Pratik12345 » Fri Mar 12, 2021 12:07 am

Ans :- 945

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Mehrab4226
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Re: BdMO National Junior 2020 P4

Unread post by Mehrab4226 » Sat Mar 13, 2021 12:33 pm

Pratik12345 wrote:
Fri Mar 12, 2021 12:07 am
Ans :- 945
You should give the solution too.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

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Zafar
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Re: BdMO National Junior 2020 P4

Unread post by Zafar » Sun Mar 14, 2021 6:52 pm

I think its 10! or 3628800
we have 10 positions and we dont know their initial positions .each of them has the same potential to obtain each position
. so the ans should be 10!

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Mehrab4226
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Re: BdMO National Junior 2020 P4

Unread post by Mehrab4226 » Mon Mar 15, 2021 12:50 am

Zafar wrote:
Sun Mar 14, 2021 6:52 pm
I think its 10! or 3628800
we have 10 positions and we dont know their initial positions .each of them has the same potential to obtain each position
. so the ans should be 10!
Not quite!
The guy in rank #1 can never win prizes other than 1st and 2nd. So, each of them DOES NOT have the same potential to obtain each position.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

131033
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Re: BdMO National Junior 2020 P4

Unread post by 131033 » Mon Mar 15, 2021 11:34 am

The answer will be: 10!-{(1+2+3+4+5+6+7+8)*9}=3628800-36*9=3628476
PROOF:
if we take three person x,y,z
then,x can obtain position 1,2
y can obtain position 1,2,3
z can obtain position 1,2,3
so,in this case the sequence number is 3!-(1*2)=6-2=4
in the same way , this answer is 3628476

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Zafar
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Re: BdMO National Junior 2020 P4

Unread post by Zafar » Mon Mar 15, 2021 1:04 pm

Mehrab4226 wrote:
Mon Mar 15, 2021 12:50 am
Zafar wrote:
Sun Mar 14, 2021 6:52 pm
I think its 10! or 3628800
we have 10 positions and we dont know their initial positions .each of them has the same potential to obtain each position
. so the ans should be 10!
Not quite!
The guy in rank #1 can never win prizes other than 1st and 2nd. So, each of them DOES NOT have the same potential to obtain each position.
But any of the persons can be at rank #1 in initial position .

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Mehrab4226
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Re: BdMO National Junior 2020 P4

Unread post by Mehrab4226 » Mon Mar 15, 2021 2:12 pm

Zafar wrote:
Mon Mar 15, 2021 1:04 pm
Mehrab4226 wrote:
Mon Mar 15, 2021 12:50 am
Zafar wrote:
Sun Mar 14, 2021 6:52 pm
I think its 10! or 3628800
we have 10 positions and we dont know their initial positions .each of them has the same potential to obtain each position
. so the ans should be 10!
Not quite!
The guy in rank #1 can never win prizes other than 1st and 2nd. So, each of them DOES NOT have the same potential to obtain each position.
But any of the persons can be at rank #1 in initial position .
No, The initial ranking is always the same.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

Naeem588
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Re: BdMO National Junior 2020 P4

Unread post by Naeem588 » Sat Apr 03, 2021 1:43 am

It's simply 2^(10-1)
lol🙃

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