ZIO 2016 Discussion

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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.

The answers were:

  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

We should have the results ready by the end of this week.

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

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?

1- 75 179 420 (Not sure about the last 2)
2- 24 48 96
3- (Got it wrong)
4- 13 10 12 (Easy one)

i got the answer 40 for 2 a)
@sandy1899 can u plz tell how u solved 1a) ?

Does anyone remember the 1st question(any part) ? I’d like to try solve it again

Well last time they got the results in 10 days so I guess it will be the same this time as well.

Well last time they got the results in 10 days so I guess it will be the same this time as well.

btw this time zio-zco were conducted together and zio was also conducted online so we can expect the result much sooner than that