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BdMO Online Forum • View topic - BDMO REGIONAL 2015

BDMO REGIONAL 2015

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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.
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BDMO REGIONAL 2015

Post Number:#1  Unread postby Math Mad Muggle » Mon Feb 06, 2017 3:39 pm

please, help me to this.....
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Re: BDMO REGIONAL 2015

Post Number:#2  Unread postby NOBODY » Mon Feb 06, 2017 5:02 pm

2 ,
118 AND 8
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Re: BDMO REGIONAL 2015

Post Number:#3  Unread postby Absur Khan Siam » Mon Feb 06, 2017 11:01 pm

Solution:
Note that there exists a number for each number such that the sum is $126$,except $2$.Thus if we take
$14$ number,we can ensure that the sum of any two number is $126$.
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid
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Re: BDMO REGIONAL 2015

Post Number:#4  Unread postby SMMamun » Tue Feb 07, 2017 4:32 pm

How did you find 14 number(s)? Did you rather mean 24? How can you find the sum 126 if you take one of the numbers to be 3?

Anyway, the phrase "the sum of any two among them" is ambiguous and does not seem to clarify what the question setters actually asked for.
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Re: BDMO REGIONAL 2015

Post Number:#5  Unread postby Absur Khan Siam » Tue Feb 07, 2017 5:00 pm

I think the statement should be "There exists a pair such
that the sum is $126$"
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid
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Re: BDMO REGIONAL 2015

Post Number:#6  Unread postby Zawadx » Mon Mar 27, 2017 8:14 pm

NOBODY wrote:2 ,
118 AND 8


You do have a point xD

The question is not properly stated. A better question would be 'Upto how many numbers must the sequence $2,3,8,13,18,23, \dots ,118$ be continued to ensure that there exists at least one pair with sum $126$'. Though that is still not perfect because the sequence is not well defined. I mean, no well-known sequence starts with $2,3,13,18,23$ The closest we have is this one :P

Or maybe the question is perfect and they want to see who has the common sense to give 2 as the answer.
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