Regional Math Olympiad 2020

For students of class 6-8 (age 12 to 14)
Tikly
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Regional Math Olympiad 2020

Unread post by Tikly » Sun Feb 21, 2021 4:00 pm

You have ten pigeons. You want to give
these pigeons away to some of your friends.
The first friend picks a number of pigeons
of her choice for herself. After that you give
away the remaining pigeons to the rest of
your friends. If you give each of them 3
pigeons, 5 are left and if you give each of

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Anindya Biswas
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Re: Regional Math Olympiad 2020

Unread post by Anindya Biswas » Mon Feb 22, 2021 3:10 pm

Please give complete problem, use the edit button.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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sakib17442
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Re: Regional Math Olympiad 2020

Unread post by sakib17442 » Wed Apr 21, 2021 7:17 pm

You have ten pigeons. You want to give these pigeons away to some of your friends. The first friend picks a number of pigeons of her choice for herself. After that you give away the remaining pigeons to the rest of your friends. If you give each of them 3 pigeons, 5 are left and if you give each of
them 5 pigeons, 3 are left. How many pigeons did your first friend choose for herself? Here is the complete problem

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sakib17442
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Re: Regional Math Olympiad 2020

Unread post by sakib17442 » Wed Apr 21, 2021 7:30 pm

This problem appeared as problem number 7 in Regional 2020 (Junior Category). This one is a quite easy problem. Okay, Here is the full solution:
Total pigeons are $10$. It means the 2nd or 3rd friend cannot take more than 10 pigeons. They can take maximum 10 pigeons. Well, in this case if you think about it, you'll figure out that 10 pigeons were distributed among 2 friends. If the second friend takes 3 pigeons, 5 pigeons are left. Such like that, if the second friend takes 5 pigeons, 3 pigeons are left. It means the after the first friend takes pigeons, 8 pigeons are left out of 10. It means the first friend took $10-8=2$ pigeons. So, the answer is 2.

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