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INMO 2017

Note by Rohit Camfar
9 months, 1 week ago

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SOLUTION TO 1

Rohit Camfar - 9 months ago

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How did you obtain the value of 'a'?

Ojasee Duble - 7 months, 3 weeks ago

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I guess you can see the last stanza of the first page of my solution. Your profile tells that your age is 14. So, I think that you are an IMO aspirant. Would you like to join us on Slack?

Rohit Camfar - 7 months, 2 weeks ago

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@Rohit Camfar Rohit could you add me on Slack. I am too an IMO aspirant.

Mithil Shah - 6 months, 1 week ago

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@Mithil Shah Ok, give @Ayush Rai your email. And you can first join the Brilliant's official team-- Click here

Rohit Camfar - 6 months, 1 week ago

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@Rohit Camfar I saw the last stanza of the first page of your solution, but I'm not getting the value of 'a' as you got after simplifying... Can you please elaborate that simplification?

And yeah, I would like to join you all :)

Ojasee Duble - 7 months, 2 weeks ago

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@Ojasee Duble

That's nice if you want to join. You can join us on slack by the end of this month as the owners are into their board exams and I am also out preparing for the exams.

Rohit Camfar - 7 months, 2 weeks ago

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@Rohit Camfar Yeah, I'll join by the end of the month. By the way, thanks for elaborating the simplification... :)

Ojasee Duble - 7 months, 2 weeks ago

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@Ojasee Duble u can give ur email id if u want to join.

Ayush Rai - 7 months, 2 weeks ago

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@Ayush Rai My email id is ojaseeduble@gmail.com

Ojasee Duble - 7 months, 2 weeks ago

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@Rohit Camfar, same as mine.

But i calculated inradius for DEH where H is intersection of D'E with AD, instead of D'EG as both are congruent or exactly copy of each other.

That was much simpler.

Priyanshu Mishra - 9 months ago

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I think there would not have been much difference in solution then.

Rohit Camfar - 9 months ago

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@Rohit Camfar Yes i said same as yours. I took side of square as 1 just for simplicity as side does not alter the proof.

Priyanshu Mishra - 9 months ago

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@Priyanshu Mishra nice solution. much differernt than mine. I think INMO problem setters like incenters.@Priyanshu Mishra why dont u join in the discussion in our team. U dont participate at all.

Ayush Rai - 9 months ago

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@Ayush Rai Where to join and chat?

Priyanshu Mishra - 9 months ago

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@Priyanshu Mishra in slack.I had invited u. u had joined it some months ago.

Ayush Rai - 9 months ago

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Problem 5:

Part 1

Part 1


Part 2

Part 2

Ayush Rai - 9 months ago

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Nice Bro!! Both ur Solution and Bedsheet!

Rohit Camfar - 9 months ago

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hahaha.lol.Thanks

Ayush Rai - 9 months ago

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Problem 1:

Ayush Rai - 9 months ago

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@Ayush Rai @Rohit Camfar - alternative method using lengths rather than angles- it uses the fact that the height from the right angle to the hypotenuse is always \(\frac{ab}{c}\), and the radius of an incircle is always \(\frac{ab}{a+b+c}\), where \(a\), \(b\) and \(c\) are the lengths of a right-angled triangle and \(c\) is the hypotenuse. Do this multiple times to prove that PQX forms an isosceles right angled triangle. You can also say that tangents that meet are the same length. Sorry I didn't write up all of the working, I'm in the middle of lunch:) Not going to lie, the geometry problems in this Indian MO are miles harder than those in the BMO, you guys are doing really well!

Dan Ley - 9 months ago

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nice one @Dan Ley

Ayush Rai - 9 months ago

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Well India is the best! And all are rest (I hope you too agree @Sharky Kesa). Well Nice solution. It is from INMO your BMO should be compared with RMO. Well try the others too @Dan Ley.

Rohit Camfar - 9 months ago

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An another thing : You wrote "Sorry I didn't write up all of the working, I'm in the middle of lunch:)" Really, are you in the middle of shool lunch?

Rohit Camfar - 9 months ago

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Of course haha I wish I lived in Asia. Is RMO easier or harder? I'll have a look at the 1st one some time, it looks fun, but no promises:) Yes it's 13:15 here! Showed my friends these questions, they're good!

Dan Ley - 9 months ago

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@Dan Ley That is easier.

Rohit Camfar - 9 months ago

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this diagram looks like ur passel of techniques problem @Rohit Camfar

Ayush Rai - 9 months ago

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hahahah Yup I remember I too thought the same. Two circles. That too was a nice one. See this if you don't know what is Passel of TechniquesFor those who haven't seen passel of techniques

Rohit Camfar - 9 months ago

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@Rohit Camfar Passel of techniques was fun;) Thanks @Ayush Rai Question: are you two at the same school?

Dan Ley - 9 months ago

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@Dan Ley Nope. He is in Bangalore and I am in JK. => IF he is in Liverpool then I am in Glasgow.

Rohit Camfar - 9 months ago

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@Rohit Camfar Haha, both Liverpool and Glasgow are very far from where I live! But I understand what you mean;) So is the RMO the first round then? We have the SMC (Senior Maths Challenge) before the BMO1 (British Mathematical Olympiad)- the top 1000 do BMO1 and the top 100 then do BMO 2;)

Dan Ley - 9 months ago

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@Dan Ley yes RMO is the first round.U are studying which class?

Ayush Rai - 9 months ago

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@Ayush Rai I study A-levels in Maths, Furthermaths, Physics and Chemistry:) Applied to University to do Engineering;) Are you still doing many different subjects?

Dan Ley - 9 months ago

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@Dan Ley Yes I have to do it for another three years.

Rohit Camfar - 9 months ago

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@Rohit Camfar Ayush has do do it for another two years. He is 1 year senior to me.

Rohit Camfar - 9 months ago

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@Rohit Camfar Wow, you're well ahead of the game for maths though- thoughts for university, do you both want to study maths?

Dan Ley - 9 months ago

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@Dan Ley Well right now I am just aiming for RMO.

Rohit Camfar - 9 months ago

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@Dan Ley dan ley, I invite u to my RMO,INMO group in slack. If u are interested u can give ur email id.

Ayush Rai - 9 months ago

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@Ayush Rai @achal jain u can also join by giving ur email address

Ayush Rai - 9 months ago

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@Ayush Rai @Dan Ley Are you interested?

Rohit Camfar - 9 months ago

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@Ayush Rai Yes we will discuss problems there. That would be fun.....

Rohit Camfar - 9 months ago

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@Dan Ley yes I want to study maths.

Ayush Rai - 9 months ago

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@Dan Ley No we aren't in the same school. Well we have a team for RMO,INMO prep. where we discuss problems in slack.

Ayush Rai - 9 months ago

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We hve got our scorecards,lets share our marks

Ayush Pattnayak - 8 months, 1 week ago

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Tell yours Ayush.. and which region are you from?

Raushan Sharma - 8 months, 1 week ago

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from Odisha

Ayush Pattnayak - 6 months ago

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I got 49- maybe I lost few marks in the 4th question where the silliest mistake of my life helped to get 4 solutions instead of 3 - of course i wouldn't have qualified even if i had got it corect.(and I had a different solution than the official ones)

Ayush Pattnayak - 6 months ago

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@Ayush Pattnayak oh thats a good score.:)

Ayush Rai - 6 months ago

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@Ayush Rai Tnx , but end of the day ,nothing to gain,right??

Ayush Pattnayak - 5 months, 1 week ago

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@Ayush Pattnayak U just gained some knowledge through ur preparations! Don't feel bad!

Ayush Rai - 5 months, 1 week ago

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i didnt write INMO

Ayush Rai - 8 months, 1 week ago

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@Ayush Rai

  1. I think the cut off must be more than 70.

Priyanshu Mishra - 7 months, 4 weeks ago

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@Priyanshu Mishra How much did you score Priyanshu??

Raushan Sharma - 7 months, 4 weeks ago

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@Raushan Sharma 54 only.

Priyanshu Mishra - 7 months, 2 weeks ago

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Problem NO 4

Rohit Camfar - 9 months ago

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Problem 5 part 2. Well first part of AYUSH is the best possible. Here is a short for 2nd one.

Rohit Camfar - 9 months ago

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Everyone lets rock. Post your solutions. Well I would like to notify some people to begin @Sharky Kesa , @Neel Khare , @Ayush Rai , @ Hrithik Nambiar , @Dan Ley , @abhishek alva Guys I don't remember anybody else's name.

Rohit Camfar - 9 months, 1 week ago

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and also @Priyanshu Mishra , @Md Zuhair

Ayush Rai - 9 months ago

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@Ayush Rai, How many you solved at INMO?

I did 1, 2,4,6 only. I am uncertain about my selection.

Priyanshu Mishra - 9 months ago

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@Priyanshu Mishra How much did you get in INMO?

Raushan Sharma - 8 months, 2 weeks ago

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@Priyanshu Mishra I didn't write Inmo.solved 1,4,5

Ayush Rai - 9 months ago

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@Ayush Rai How you got 5?

Priyanshu Mishra - 9 months ago

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@Priyanshu Mishra You can see above?

Rohit Camfar - 9 months ago

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