Kertoma

#include <bits/stdc++.h>

typedef long long ll;

#define M 1000000007
#define N (1 << 18)

using namespace std;

// Num of digits :D

ll nums[10];

bool check(string num) {
    vector<int> v(10);
    for (int i = 0; i < (int)num.length(); ++i) {
        v[num[i] - '0']++;
    }

    for (int i = 0; i < 10; ++i) {
        if (v[i] != nums[i]) return false;
    }

    return true;
}

int brute() {
    ll fct = 1;
    for (ll mul = 2; mul <= 20; ++mul) {
        fct *= mul;
        if (check(to_string(fct))) {
            return mul;
        }
    }
    return -1;
}

ll digits(ll fct) {
    double ans = 0;
    for (ll i = 1; i <= fct; ++i) {
        ans += log10(i);
    }

    return ans + 1;
}

ll fast(ll sum) {
    for (ll fct = 2; fct <= 100000; ++fct) {
        if (digits(fct) == sum) return fct;
    }
    return -1;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    ll sum = 0;
    for (int i = 0; i < 10; ++i) {
        cin >> nums[i];
        sum += nums[i];
    }

    if (sum <= 15) {
        cout << brute() << endl;
        return 0;
    }

    cout << fast(sum) << endl;

    return 0;
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

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