C++ :

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

const int MAXN = 5, MAXW = 5;
struct Wheel {
    int speed;
    vector<pair<int, int> > gap;
};
int N, flag[360];
Wheel W[MAXN];

int main()
{
     freopen("spin.in", "r", stdin);
     freopen("spin.out", "w", stdout);
     N = MAXN;
     for (int i = 0; i < N; i++) {
          int tot_gap; scanf("%d%d", &W[i].speed, &tot_gap);
          for (int j = 0; j < tot_gap; j++) {
               int start, len; scanf("%d%d", &start, &len);
               W[i].gap.push_back(make_pair(start, len));
          }
     }

     bool find = false;
     for (int t = 0; t < 360 && !find; t++) {
          memset(flag, 0, sizeof(flag));
          for (int i = 0; i < N; i++) {
               const int &speed = W[i].speed;
               vector<pair<int, int> > &gap = W[i].gap;
               for (int j = 0; j < gap.size(); j++) {
                    for (int k = 0; k <= gap[j].second; k++)
                         flag[(gap[j].first + k) % 360]++;
                    gap[j].first = (gap[j].first + speed) % 360;
               }
          }
          for (int i = 0; i < 360; i++)
               if (flag[i] == N) {find = true; printf("%d\n", t); break;}
     }
     if (!find) printf("none\n");
     fclose(stdin); fclose(stdout);
     return 0;
}