ZIO 2016 Discussion

general
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41

whats the cut off?

42

For 1) The answers are definitely a) 75 b) 175 and c) 399

1 Like
43

Hey here are my answers:-

  1. 75 , 175 , 399
  2. 38 , didnā€™t solve , didnā€™t solve
  3. 71 , 461 , 3447
  4. 13 , 10, 12
    Todayā€™s paper was bad , kids from RDPS were cheating rampantly , some people around me were coding in Dev and getting the output, IIITD shouldā€™ve been the center , no invigilation whatsoever and paper shouldā€™ve been written.
44

Hey guys Iā€™m in class 11. Please tell us your class too cause then we can make an approximation for the cut off as it varies class to classā€¦ Also Iā€™m expecting 40/80 :frowning:

45

@dmhero My bad, I double counted some case, the answer for first subproblem is 36.

Method: Combinatorics

For the first row you have 3 choices and for the following rows until the last you have 2 choices.
For the last row you have only 1 choice.(You pick red if the count for red is odd upto the last row and donā€™t pick red if count is odd)

So for the 2nd subproblem
3 * 2 * 2 * 2 * 2 * 1=48

For the 3rd subproblem
3 * 2 * 2 * 2 * 2 * 2 * 1=96

In the first problem the red on the last row is below the red on the previous row. So you have subtract some cases.

Hope this solution is correct.

46

@sandy1899

Yep this seems to be correct I spent a lot of doing this problem manually but I miscounted and got 38 as the answer :ā€™ā€™(

47

im in class 10 n expecting 25

48

Q1. 1) 75 2)175 3)399 (i wrote 400 though)

Q2. 1) 36 not sure about any answer here would like some clarity

Q3. all wrong
Q4. !) 13 2) 10 3) 12

11th grade - expecting 30

PS. Could someone give a definitive answer for question 2 and a valid method (ideally not brute force)

49

Yes 36 seems to be correct I counted it manually as well however I wrote the answer as 38,I got for R = 0, 2 ways,for R = 2, 24 ways , R = 4, 10 ways. Total 2+10+24 = 36

50

@r4huln how much score are u expecting along with ur class?

51

15 class 10 I made 2 very silly mistakes in sub problems or else I could have got 30 so surely i am not qualifying

52

I donā€™t remember my solutions but hereā€™s my algorithm for Problem 2,

Let n represent the number of columns.

Let f(i, 1) represent the number of paths ending at peg 1 of column i while red count is even. Similarly for f(i, 2) and f(i, 3).

Let g(i, 1) represent the number of paths ending at peg j of column i while red count is odd. Similarly for g(i, 2) and g(i, 3).

We want to find ā€”> f(n, 1) + f(n, 2) + f(n, 3)

Here is the recursive function :

If peg at (i, 1) is red, then f(i, 1) = g(i-1, 2) + g(i-1, 3) and g(i, 1) = f(i-1, 2) + f(i-1, 3). Similarly for pegs (i, 2) and (i, 3).

else f(i, 1) = f(i-1, 2) + f(i-1, 3) and g(i, 1) = g(i-1, 2) + g(i-1, 3). Similarly for pegs (i, 2) and (i, 3).

Using this, we solve the problem bottom-up.

For instance(I just made this up to demonstrate how this works),

1       2        3        
R       B        B        
G       R        G        
B       R        B

Base cases are

f(1, 1) = 0, g(1, 1) = 1

f(1, 2) = 1, g(1, 2) = 0

f(1,3) = 1, g(1, 3) = 0

Now, we look at the 2nd column.

f(2, 1) = 1 + 1 = 2, g(2, 1) = 0 + 0 = 0

f(2, 2) = 1 + 0 = 1, g(2, 2) = 0 + 1 = 1

f(2, 3) = 1 + 0 = 1, g(2, 3) = 0 + 1 = 1

Now we look at the 3rd column(note that we only need f(n, i) to compute the final answer and so, we donā€™t calculate g(n, i))

f(3, 1) = 1 + 1 = 2

f(3, 2) = 2 + 1 = 3

f(3, 3) = 1 + 2 = 3

Finally, our answer is 2 + 3 + 3 = 8.

53

@excudeles marks with class

54

@dmhero

Itā€™s sad. I made a silly mistake in P3 by not looking at a case and so, all my answers to that question are off by a few numbers. My P4 is correct and same as you guys. Assuming I made no calculation errors in P2(which is possible), Iā€™ll get a 40. And Iā€™m in class 12th. I have very low chances of getting through.

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@sandy1899

Your method for P2 is clearly wrong.

56

Probably the cutoffs will be 5 points lower than last yearsā€™ - for each class.

57

@animesh_f probably yes, people made alot of mistakes and it certainly was tough

58

Firstly, Iā€™m in Class 9ā€¦

I did Question 4 all correct but Iā€™m not sure about Question 1 and 2. 3 screwed up completely (Didnā€™t take a case into account resulting in wrong answers)

For 1 got 80, 192 and 448. What is supposed to be the correct answer here? (Many people have given different answers)

For 2, 36, 49 and 96. 96 seems to be correct and some other people have got 36 as well (brute force, could have used combinatorics but I kinda screwed up)

Worst case scenario, Iā€™m expecting 25 (96 + Question 4)
Although I think Iā€™ve done Question 2 correctlyā€¦

Any ideas about the cutoff? (I hope it is 25ā€¦)

59

Correct answers:

1 - 75, 175, 399

2 - 40, 52, 96

3 - 71, 461, 3447

4 - 13, 10, 12

4 Likes
60

im sure about 75 though not getting it