Problem: Example

Input

0 3 1 7 5 9 8 6 4 2
7 0 9 2 1 5 4 8 6 3
4 2 0 6 8 7 1 3 5 9
1 7 5 0 9 8 3 4 2 6
6 1 2 3 0 4 5 9 7 8
3 6 7 4 2 0 9 5 8 1
5 8 6 9 7 2 0 1 3 4
8 9 4 5 3 6 2 0 1 7
9 4 3 8 6 1 7 2 0 5
2 5 8 1 4 3 6 7 9 0


Output

0

Solution (in CPP):

Solution:
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)

int main() {
    vector<vector<int>> t(10, vector<int>(10));
    for (auto &ti: t) for (auto &tij: ti) cin >> tij;
    auto calc = [&](vector<int> &a) {
        int ret = 0;
        rep(i, 4) ret = t[ret][a[i]];
        return ret;
    };
    auto is_zero = [&](vector<int> &a) { return t[calc(a)][a.back()] == 0; };
    auto can_detect = [&](vector<int> &a) {
        // altering one single digit
        vector<int> b = a;
        rep(i, 5) rep(err, 10) if (a[i] != err) {
            b[i] = err;
            if (is_zero(b)) return false;
            b[i] = a[i];
        }
        // transposing two adjacent digits
        rep(i, 4) if (a[i] != a[i + 1]) {
            swap(b[i], b[i + 1]);
            if (is_zero(b)) return false;
            swap(b[i], b[i + 1]);
        }
        return true;
    };
    int cnt = 0;
    rep(a, 10) rep(b, 10) rep(c, 10) rep(d, 10) {
        vector<int> v{a, b, c, d};
        v.emplace_back(calc(v));
        cnt += !can_detect(v);
    }
    cout << cnt << endl;
    return 0;
}