INMO 2017

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Problem 5:
Part 1 Part 1
Part 2 Part 2

Ayush G Rai - 4 years, 5 months ago

Nice Bro!! Both ur Solution and Bedsheet!

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

hahaha.lol.Thanks

Ayush G Rai - 4 years, 5 months ago

SOLUTION TO 1

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@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 - 4 years, 4 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@Vishwash Kumar Γξω – 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 - 4 years, 4 months ago

@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 G Rai - 4 years, 4 months ago

@Ayush G Rai – Where to join and chat?

Priyanshu Mishra - 4 years, 4 months ago

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

Ayush G Rai - 4 years, 4 months ago

How did you obtain the value of 'a'?

Ojasee Duble - 4 years, 3 months ago

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?

Vishwash Kumar ΓΞΩ - 4 years, 3 months ago

@Vishwash Kumar Γξω – 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 - 4 years, 3 months ago

@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.

Vishwash Kumar ΓΞΩ - 4 years, 3 months ago

@Vishwash Kumar Γξω – Yeah, I'll join by the end of the month. By the way, thanks for elaborating the simplification... :)

Ojasee Duble - 4 years, 3 months ago

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

Ayush G Rai - 4 years, 3 months ago

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

Ojasee Duble - 4 years, 3 months ago

@Vishwash Kumar Γξω – Rohit could you add me on Slack. I am too an IMO aspirant.

mithil shah - 4 years, 2 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 2 months ago

@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 - 4 years, 5 months ago

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.

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

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?

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

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 - 4 years, 5 months ago

@Dan Ley – That is easier.

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

nice one @Dan Ley

Ayush G Rai - 4 years, 5 months ago

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

Ayush G Rai - 4 years, 5 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

@Vishwash Kumar Γξω – Passel of techniques was fun;) Thanks @Ayush Rai Question: are you two at the same school?

Dan Ley - 4 years, 5 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

@Vishwash Kumar Γξω – 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 - 4 years, 4 months ago

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

Ayush G Rai - 4 years, 4 months ago

@Ayush G 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 - 4 years, 4 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@Vishwash Kumar Γξω – Ayush has do do it for another two years. He is 1 year senior to me.

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@Vishwash Kumar Γξω – Wow, you're well ahead of the game for maths though- thoughts for university, do you both want to study maths?

Dan Ley - 4 years, 4 months ago

@Dan Ley – yes I want to study maths.

Ayush G Rai - 4 years, 4 months ago

@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 G Rai - 4 years, 4 months ago

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

Ayush G Rai - 4 years, 4 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@Ayush G Rai – @Dan Ley Are you interested?

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@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 G Rai - 4 years, 5 months ago

Problem 1:

Ayush G Rai - 4 years, 4 months ago

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.

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

and also @Priyanshu Mishra , @Md Zuhair

Ayush G Rai - 4 years, 4 months ago

@Ayush Rai, How many you solved at INMO?

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

Priyanshu Mishra - 4 years, 4 months ago

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

Ayush G Rai - 4 years, 4 months ago

@Ayush G Rai – How you got 5?

Priyanshu Mishra - 4 years, 4 months ago

@Priyanshu Mishra – You can see above?

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

@Priyanshu Mishra – How much did you get in INMO?

Raushan Sharma - 4 years, 4 months ago

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

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

Problem NO 4

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

We hve got our scorecards,lets share our marks

Ayush Pattnayak - 4 years, 4 months ago

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

Raushan Sharma - 4 years, 4 months ago

i didnt write INMO

Ayush G Rai - 4 years, 4 months ago

@Ayush G Rai –

I think the cut off must be more than 70.

Priyanshu Mishra - 4 years, 3 months ago

@Priyanshu Mishra – How much did you score Priyanshu??

Raushan Sharma - 4 years, 3 months ago

@Raushan Sharma – 54 only.

Priyanshu Mishra - 4 years, 3 months ago

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 - 4 years, 1 month ago

@Ayush Pattnayak – oh thats a good score.:)

Ayush G Rai - 4 years, 1 month ago

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

Ayush Pattnayak - 4 years, 1 month ago

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

Ayush G Rai - 4 years, 1 month ago

from Odisha

Ayush Pattnayak - 4 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$