Rmo was conducted on 9th October in Gujarat.

1)Let ABC be a right angled triangle with B=90°.Let I be tye incentre of ABC.Let AI extended intersect BC at F.Draw a line perpendicular to AI at I.Let it intersect AC at E.Prove that IE=IF.

2)Let a,b,c be positive reals such that

```
(a/1+b)+(b/1+c)+(c/1+a)=1
```

Prove that abc≤1/8.

3)For any natural number n,expressed in base 10,let S(n) denote the sum of all digits of n.Find all natural numbers n such that

n³=8S(n)³+6nS(n)+1.

4)How many 6 digit natural numbers containing only the digits 1,2,3 are there in which 3 occurs exactly twice and the number Is divisible by 9?

5)Let ABC be a right angled triangle with B=90°.Let AD be the bisector of A with D on BC.Let the circumcircle of triangle ABD intersect AC again in E,and let the circumcircle of triangle ABD intersect AC again in F.Let K be the reflection of E in the line BC.Prove that FK=BC.

6)Show that the infinite arithmetic progression (1,4,7,10......) Has infinitely many 3-term subsequences on harmonic progression such that for any two such triples (a,b,c) and (p,q,r) in harmonic progression ,one has a/p≠b/q.

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## Comments

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TopNewestGuys today is INMO may the best get selected

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Hey guys! The RMO 2016 results are out, who all made it to INMO. Pls do create notes and discussion for the upcoming INMO. Thank you. @Harsh Shrivastava@naitik sanghavi@Mayank Jha@Rajdeep Dhingra@Anik Mandal@Swapnil Das

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I got selected for inmo !!!!

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I suggest pls ask someone who has prior experience of INMO.He could guide all of us in a better way

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You may post the inmo practice board note.

Only about 1 month left!

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I didn't appear RMO, sorry.

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I qualified RMO from Tamilnadu region !!! Can you guys post an INMO practice board soon ? Only around a month left .

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Guys I scored 41/102 .My questions were the same as mentioned above even though I belong to a different region. Do I stand a fair chance of qualification ?

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please post the solution for second one

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Thanks! In the 4th q, I ended up writing "NO no. will be possible.." instead of "0". Idiotic, I know. Let's wait for results now.

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Do the RMO answer sheet checkers cut marks for long methods, provided they have a very short method in their answer key? Any idea how many will be selected for INMO this year from Gujarat?

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Dont know about checking but I think they would cut some marks for that!30-35 will be selected and top 5 girl students extra!

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Yeah that's for sure. But don't worry about that first of all be joyful.

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Did any one get the 6th one ?

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Is 17 the only possible answer for q3 ?

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Yes.

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All the best for your RMO !!!

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How many of you people got fifth one ?????

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Is q4 answer 0? As the number is divisible by 9 sum of remaining 4 digits +6 must me divisible by 9 but no case is satisfied

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Yeah, the answer is zero

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1st one is done. help for q6.

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Can someone give solution to q1 and q6

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Join I and C in first one

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Guys did anyone get the 3rd one ?????

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Hint: a+b+c=0 if a^3+b^3+c^3-3abc=0

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Did you get any solutions

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here

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Can someone provide a hint/solution to problem 6?

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I did it but I have no gaurantee whether I am right or not. : )

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Guys check out the telangana paper same as this one. No change

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Are we allowed to use Titu's lemma, Chebyshev's inequality,Holder,etc. to solve inequality problems?

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But it can be done through AM GM and cauchy inequality : )

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Yeah why not.

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What do you all think will bebl the cutoff for this region?Last years cutoff was 31 and approx 30-40 in past years !!

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Should be greater than 50.

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Can someone post a solution to the inequality question number 4 in the delhi paper?

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RMO 2016 Delhi Region http://rmonorthzone.com/RMO

2016Delhi_zone.pdfRMO 2016 Maharashtra and Goa Region Problems https://doc-0o-ao-docs.googleusercontent.com/docs/securesc/ha0ro937gcuc7l7deffksulhg5h7mbp1/5353lnd22lup3lvu0eqb2f0a7tqb7ucf/1476158400000/01355186314162261890/

/0BzLwescIQp6cbzQ3UG1vMElSb2M?e=download Solutions https://doc-0c-ao-docs.googleusercontent.com/docs/securesc/ha0ro937gcuc7l7deffksulhg5h7mbp1/j1l5kkjqoutlkrq6f1cs5r899sfao56f/1476158400000/01355186314162261890//0BzLwescIQp6cOVBpRXFtaVpOMDA?e=downloadRMO 2016 Mumbai Region http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvMy85L2Q1NGE2ZjA4ZTY4YWZkZmE5ZDA0OTFlOTBkOGQyNmM1NGMxYTlmLmpwZw==&rn=U2Nhbl8yMDE2MTAwOS1taW4uanBn

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@Kush Singhal Here you go . . . . http://www.artofproblemsolving.com/community/c260h1228775s1

rmo2016andinmo2017preparation_group 566th postLog in to reply

Thanx

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Q1 seems to be very easy . . . .

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In the 5th question, it says that K is the reflection of "E" in BC. But what is "E"? Could it be F?

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Kush singhal E is intersection of AB with circumcircle of ACD

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I found the maharashtra and goa region question paper along with a solution pdf here: http://www.rmomah.org/ I found the delhi region question paper here: http://rmonorthzone.com/RMO

2016Delhi_zone.pdf I'm still searching for the greater mumbai region's question paper...., if anyone knows where it could be posted could you please tell me?Log in to reply

Can you please re-post the question 5, it is not clearly stated.

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Done

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This year's paper is very easy.

I have my rmo on 16th.

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Although I didn't try to solve the Delhi Paper, it seems to be quite hard!

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try question no. 4 of Delhi zone

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When is your rmo?

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Where is it posted?

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Here The paper is posted somewhere in the 600-750th post so you need to keep scrolling down!

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Haa! Best of luck for your Rmo! BTW in which standard r u?

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11th. Wbu?

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The fourth question as it is currently given ^ admits a trivial solution of 0 The condition of exactly two 3's and digits only being 1,2,3 forces the digit sum to be bounded between 10 and 14, and so the number can never be divisible by 9... Is there some typing error?

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No, it was exactly the same as written on question paper. Everyone asked in exam hall if it had any corrections! I was shocked!!! So I think this year our regions cutoff will go high!

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