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.