C++ Choose a Door

#include <iostream>
#include <ctime>
#include <cmath>
#include <iomanip>
#include <climits>

//Make a code with 3 CPUs. Choose a door and try to get a door none of the CPUs choose. Add a new door each round until the player wins.

int cpu(int door);
int door(int round);
void doorCount(int door);
bool doorCheck(int doorChoice, int cpuDoor);
void cpuStillAlive(bool cpu, int cpuDoor, int cpuNum);

int main() {

    srand(time(0));

    int round = 1;
    int doors = 0;
    int doorChoice = 0;
    int cpu1door = 0;
    int cpu2door = 0;
    int cpu3door = 0;
    bool cpu1 = true;
    bool cpu2 = true;
    bool cpu3 = true;

    std::cout << "**Welcome to Choose a Door!**\n\n";
    std::cout << "Rules: Choose a door and eliminate all the CPUs before time runs out!\n";

    do{
        doors = door(round);

        std::cout << '\n';

        if(doors == 1) {
            break;
        }

        if(doors > 2){
            std::cout << "Round " << round << "!\n";
        }
        else if(doors == 2){
            std::cout << "Final Round!\n";
        }



        doorCount(doors);
        do {
            std::cin >> doorChoice;
            std::cin.clear();
            std::cin.ignore(INT_MAX,'\n');
        }while (doorChoice < 1 || doorChoice > doors);



        if(cpu1 == true) {
            cpu1door = cpu(doors);
            cpu1 = doorCheck(doorChoice,cpu1door);
            cpuStillAlive(cpu1, cpu1door, 1);
        }

        if(cpu2 == true) {
            cpu2door = cpu(doors);
            cpu2 = doorCheck(doorChoice,cpu2door);
            cpuStillAlive(cpu2, cpu2door, 2);
        }

        if(cpu3 == true) {
            cpu3door = cpu(doors);
            cpu3 = doorCheck(doorChoice,cpu3door);
            cpuStillAlive(cpu3, cpu3door, 3);
        }

        if(cpu1 == true || cpu2 == true || cpu3 == true){
            round++;
        }

    }while(cpu1 == true || cpu2 == true || cpu3 == true);

    if(cpu1 == true || cpu2 == true || cpu3 == true) {
        std::cout << "\nCPUs win!";
    }
    else {
        std::cout << "\nPlayer wins!";
    }

    return 0;
}

int cpu(int door) {
    int doorChoice;

    doorChoice = rand() % door + 1;

    return doorChoice;
}

int door(int round) {
    int door;

    //Start with 10 Doors
    //Subtract a door each round.
    for(int i = 1; i <= (11 - round); i++){
        door = i;
    }

    return door;
}

void doorCount(int door) {
    for(int i = 1; i <= door; i++){
        if(i % 3 != 0) {
            std::cout << i << ": Door " << i << '\t';
        }
        else{
            std::cout << i << ": Door " << i << '\n';
        }
    }
}

bool doorCheck(int doorChoice, int cpuDoor) {
    bool cpuSafe = true;

    if(doorChoice == cpuDoor) {
        cpuSafe = false;
    }

    return cpuSafe;
}

void cpuStillAlive(bool cpu, int cpuDoor, int cpuNum){
    std::cout << "CPU " << cpuNum << " chose " << cpuDoor << "! ";

    if(cpu == true) {
        std::cout << "CPU " << cpuNum << " is still in!\n";
    }
    else{
        std::cout << "CPU " << cpuNum << " is out!\n";
    }
}