UPDATE1:reults: https://www.iarcs.org.in/inoi/2019/zio2019/results_zio2019.php

UPDATE2:questions: https://www.iarcs.org.in/inoi/2019/zio2019/zio2019-question-paper.pdf

ANSWERS/CUTOFF:https://www.iarcs.org.in/inoi/2019/zio2019/zio2019-solutions.pdf

Hi how was Zio if possible post it answers

Post ur zio scores here

https://docs.google.com/spreadsheets/d/16FhkEfKr5gM0MPErxEuxpHw1TYlHM8j8tKpm3LFhSXc/edit?usp=sharing

Mostly accepted answers(from discuss and ICO whatsapp group)

1a.**69** 1b.**105** 1c.**133**

2a.**8** 2b.**7** 2c.**11**

3a.**198** 3b.**520** 3c.**1363**

4a.**144** 4b. **8192** 4c. **1638400**

**Question 4**: NĂ—N array with -1 and 1

It is magical if exactly 1 column, 1 row has product =-1 all other column and row product =1.

For a given N find no magical grids.

4a.N=3 4b. N=4 4c. N=5

**Solution 4:** **Fix** the **ROW** and **COLUMN** that have the **Product of elements** =**-1**;

Now **RANDOMLY** fill 1,-1 in remaining cells.

The no of such possibility =**2^{(n-1)^2}**;

Now leave the **intersection** **cell**(of selected row and column) other than that for each cell in the selected row and column the value of that cell is fixed. ( Since the **product of elements in REMAINING row or column needs to be =1**)

**Now sign of intersection cell is also fixed**.

Proof:**Product of all elements in grid EXPECT than selected ROW and COLUMN** and **Product of elements in ROW except the INTERSECTION** is **SAME**.

Because the product of all other columns except selected COLUMN is 1

Similarly

**Product of all elements in grid EXPECT than select ROW and COLUMN** and **Product of elements in COLUMN except the INTERSECTION** is **same**.

Which implies

**Product of elements in COLUMN except for the INTERSECTION**

And

**Product of elements in ROW except the INTERSECTION** is **same**

So if that product of elements in Selected ROW expect INTERSECTION is -1 value of INTERSECTION cell is 1

Else it is -1

So if we fix ROW and COLUMN whose product is -1 and the fix the REMAINING cells then selected Row and column can be filled in only one way.

so **Total no such GRIDS possible =no of ways of choosing row and column Ă— no ways of filling remaining cells**.

**Total no such GRIDS possible**=n^22^{(n-1)^2}

**question 1:** Given integer N.

Take first N natural numbers

Find no subsequence such that in that subsequence a[i-1] divides a[i] for all i in that subsequence?

1a.N=15 1b.N=19 1c.N=22

**Solution 1**: Have dp[i]=no of such subsequence ending with the last element as i;

If i is prime dp[i]=2.

else dp[i]=2+dp[all the factors of i];

**ans=summation all dp[] till N;**

Thanks, @kayak for the solution for question 4.