Kertoma

#include <iostream>
#include <math.h>

#define FUCTION(x) (floor(log10( sqrt(2 * M_PI * floor(x)) ) + x * log10(floor(x) / M_E)) + 1)

int main() {

    int digits = 0;
    int n;
    unsigned int i_d[10]; // indivitual_digits

    for (int i = 0; i < 10; i++) 
    {
        std::cin >> n;
        i_d[i] = n;
        digits += n;
    }

    if (digits < 4)
    {
        if      (i_d[2] == 1 && i_d[7] == 1)    std::cout << 6 << '\n';
        else if (i_d[2] == 1 && i_d[1] == 1)    std::cout << 5 << '\n';
        else if (i_d[2] == 1 && i_d[4] == 1)    std::cout << 4 << '\n';
        else if (i_d[6] == 1)                   std::cout << 3 << '\n';
        else if (i_d[2] == 1)                   std::cout << 2 << '\n';

        while (true) {}

        return 0;
    }

    int prediction = 0.5 * (digits - 185) + 113;
    int difference = digits - FUCTION(prediction);
    int start = prediction, end = prediction;

    if (difference > 0) end   += difference;
    else                start += difference;

    while (difference != 0) // 234 744 674 231 747 542 122 634 123 977
    {
        prediction = floor(start + (end - start) / 2.0f);
        difference = digits - FUCTION(prediction);

        if (difference > 0) start  = prediction;
        else                end    = prediction;

        // std::cout << "Better Luck Next time!\n";
    }

    std::cout << prediction << '\n';
    return 0;
}

Test 1

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 2

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 3

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 16

Group: 3

Verdict: TIME LIMIT EXCEEDED