# ZIO 2016 Discussion

How was the exam for all of you ?
I don’t think that I’ll get selected, it was a easy paper but wasted alot of time.

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Which questions were you able to solve? I attempted 2, 3 and 4 although I don’t remember the answers at all.

Me too, i made a stupid decision to not try question 4 alot.

It was bad for me too…
So guys what are the answers ya’ll got?

1. Binary : 80 , 192 , 448 == All wrong… Over counted repetitions by mistake
2. RGB Board game : 42 , 58 , 76 == No idea how…
3. King and Minister : 71 , ~400(forgot :P) , 3447 == Used recursion… need someone to verify though
4. Lists : 13 , 10 , 12(NOT SURE OF ORDER) == Easy one

Guys please check and share your results… What do you think the cut off is going to be this year?

I got these answers. Maybe some are wrong.
1.a 75 1.b 175 1.c 398
2.a 44 2.b 58 2.c Did not attempt
3.a 80 3.b 512(most probably) 3.c Forgot what i got. It was a 4 digit number starting with 3 and ending with 8.
4.a 13 4.b 10 4.c 12

1- a-80 b-192 c-448 (All wrong)

2- a-40 b-52 c-96 (Not sure whether correct or not)

3- Did not attempt

4- a-13 b-10 c-12 (Seems to be correct after seeing other’s answer)

Please somebody tell me how much did i scored and what are the correct answers

can any1 remember what was the binary subset in the 1st question?

then the answers are 1 a) 80
b)192
c=448

n hey what are ur respective classes?

Can anyone who solved the third question post their method? Looks like everyone’s getting different results on that one.

well i did them like that…
let X=11011
so a binary sequence of 9 dig would be of forms
X _ _ _ _
_ X _ _ _
_ _ X _ _
_ _ _ X _
_ _ _ _ X
so this is a case of permutations where repitition is allowed
so the permutations of 0 and 1 in the blanks would be 2^4
as the position of x is independent of position of the permutations of the other binary digits,
the ans is 5*(2^4)=80

can someone post the questions?

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@dmhero

I believe your method is wrong. You’re doing some double counting this way. For instance, (11011)0110 is the same as 110(11011)0.

@excudeles
got it.

Today’s P3 (King and Minister) was actually INMO 1992 P4 (k=6).
You can check out the discussion on AOPS here.

These are called indecomposable permutations; one can solve for the number of them of a given length using generating functions, or use a recursion. They are given by sequence A003319 in the OEIS.

1. 71
2. 461
3. 3447

1 a. 80 b. 192 c. 448 - ✗
2 a. 40 b. 52 c. 96 - ✓
3 a. 71 b. 461 c. 3447 - ✓
4 a. 13 b. 10 c. 12 - ✓

I think I scored 60, I’m in class 12.

Also, this

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Guys what about problem 2?
Great to know I know I got P3 fully correct

What do you reckon the cutoff will be?

I think in the range of 25-35 from 10th to 12th so 25 for 10th and 30 for 11th and 35 for 12th as last year’s was much easier and the cutoff range was 35-45.

when r the results supposed to come out?

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