Problem 1. Consider the following game for two players Pl and P2. P1 picks an in

Question

Problem 1. Consider the following game for two players Pl and P2. P1 picks an integer i between 1 and an upper limit k. P2 tries to determine i by a series of guesses. A guess consists of P2 naming a number j and P1 stating whether J 1. The game is over when P2 guesses J-1 Assuming an optimal strategy is used, how many guesses does P2 need in order to be sure to Briefly explain each of your answers. find i in each of the following cases? 1, k= 1023. 2, k = 1023 and P1 tells P2 before the first guess that i is even. 3. k = 1023 and PI tells P2 after answering the second guess that i is even. 4, k = 2047 and Pi tells P2 before the first guess that i is divisible by 8. 5. k = 255 and P1 tells P2 be 6. A = 64 and Pi tells P2 before the first guess that i is a power of 2, that is, t-2p for some p 20. z+. fore the first guess that i is a square number, that is, vi

Explanation / Answer

There are total 6 programs:

1.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));

    int a = rand()%1023;
    count = 0;
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

2.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));

    int a = rand()%1023;

    while (a%2!=0)
         a = rand()%1023;
    count = 0;
    cout << "The number is even ";
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

3.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));

    int a = rand()%1023;

    while (a%2!=0)
         a = rand()%1023;
    count = 0;
   
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
        
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
         if (count ==2)
            cout << "The number is even ";
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

4.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));

    int a = rand()%2047;

    while (a%8!=0)
         a = rand()%2047;
    count = 0;
    cout << "The number is divisible by 8 ";
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
        
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
        
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

5.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));
    int a;

  
    int rem = 1;
    int i = 2;
    while (rem!=0){
        a = rand()%255;
        for (int i = 1; i<15; i++){
           if (a % i == 0){
               rem = 0;
               break;
           }
        }
    }
    count = 0;
    cout << "The number is a square number ";
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
        
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
        
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

6.

#include<iostream>
#include<stdlib.h>
#include<time.h>

using namespace std;

int main(){

    int k,count,guess;
    srand(time(NULL));
    int a;

  
    int rem = 1;
    int i = 1;
   
    while (rem!=0){
        a = rand()%64;
        i = i * 2;
        rem = a % i;

    }
    count = 0;
    cout << "The number is a power of 2 ";
    while(1){
         cout << "Enter your guess :";
         cin >> guess;
         count++;
        
         if (a == guess)
            break;
         if (guess > a){
            cout <<"Guess is high" << endl;
         }
         if (guess < a){
            cout <<"Guess is low" << endl;
         }
        
    }
    cout << "Your guessed it right. Yout guess count is " << count << endl;
   
}

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