# PROBLEM LINK:

Contest Division 3

Contest Division 4

**Setter and Editorialist :** Yashodhan Agnihotri

# DIFFICULTY:

1121

# PREREQUISITES:

None.

# PROBLEM:

Find the maximum number of pooks on an N x N chessboard such that none of them threaten each other. A Pook has the properties of both, a pawn and a rook.

# EXPLANATION:

We will see 4 cases here. The three cases of N = 1,2,3 need to be handled separately while N \geq 4 will follow the answer of the N-Queen Problem. Since we can place atmost N unthreatening rooks on a N x N chessboard, therefore as a Pook has all the properties of Rooks, we would be able to place atmost N pooks as well.

The answer for the N-Queen problem for N greater than 4 is N queens, therefore our answer will also be the same here.

## N = 1

Since there is just one square, we can place 1 pook in it.

## N = 2

Here, we can place just 1 pook, since all the other three squares will be threatened by it.

## N = 3

Here, however you place the pooks, you cannot place more than 2 pooks on the board.

## N >= 4

Here, the answer is same as the N-Queen Problem i.e N pooks.

# SOLUTIONS:

## Setter's Solution

```
#include<bits/stdc++.h>
using namespace std;
int main() {
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
if (n == 2 || n == 3)
cout << n - 1 << "\n";
else
cout << n << "\n";
}
return 0;
}
```

For doubts, please leave them in the comment section, I’ll address them.