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
please, help me to this.....
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 Posts: 65
 Joined: Tue Dec 08, 2015 4:25 pm
 Location: Bashaboo , Dhaka
Re: BDMO REGIONAL 2015
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 $126$.
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
Re: BDMO REGIONAL 2015
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.
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.

 Posts: 65
 Joined: Tue Dec 08, 2015 4:25 pm
 Location: Bashaboo , Dhaka
Re: BDMO REGIONAL 2015
I think the statement should be "There exists a pair such
that the sum is $126$"
that the sum is $126$"
"(To Ptolemy I) There is no 'royal road' to geometry."  Euclid
Re: BDMO REGIONAL 2015
You do have a point xDNOBODY wrote:2 ,
118 AND 8
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 wellknown sequence starts with $2,3,13,18,23$ The closest we have is this one
Or maybe the question is perfect and they want to see who has the common sense to give 2 as the answer.