problem 31

/*
n England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
How many different ways can £2 be made using any number of coins?
*/
#include <iostream>
using namespace std;


int main() {
  int counter = 0;
  int p_200 = 200;
  for(int a = p_200; a >= 0; a -= 200){
    for(int i = a; i >= 0; i-= 100){
    for(int j = i; j >= 0; j-= 50){
      for(int x = j; x >= 0; x-= 20){
        for(int y = x; y >= 0; y-= 10){
          for(int z = y; z >= 0; z-= 5){
            for(int n = z; n >= 0; n-= 2){
              counter++;
              
            }
          }
        }
      }
    }
  }
  }
  
  cout << counter <<endl;
  return 0;
}