Calculate 24 points.

24.cc

#include <boost/rational.hpp>
#include <iostream>
#include <vector>
#include <stdio.h>

using boost::rational;
using std::cout;
using std::vector;
typedef vector<rational<int>> Numbers;

bool is_integer(rational<int> x)
{
  return x.denominator() == 1;
}

void calc(rational<int> x, rational<int> y, Numbers& result)
{
  result.clear();
  result.push_back(x+y);
  result.push_back(x*y);

  if (x >= y)
    result.push_back(x-y);
  else
    result.push_back(y-x);

  const bool kAllowRational = true;
  if (x != 0 && (kAllowRational || is_integer(y/x)))
    result.push_back(y/x);
  if (y != 0 && (kAllowRational || is_integer(x/y)))
    result.push_back(x/y);
}

bool g_track = false;

bool check(const Numbers& input)
{
  if (input.size() == 1)
  {
    if (input[0] == 24)
      return true;
  }
  else
  {
    Numbers next;
    Numbers result;
    for (size_t i = 0; i < input.size(); ++i)
      for (size_t j = i+1; j < input.size(); ++j)
      {
        calc(input[i], input[j], result);
        for (auto x : result)
        {
          next.push_back(x);
          for (size_t k = 0; k < input.size(); ++k)
          {
            if (k != i && k != j)
              next.push_back(input[k]);
          }
          assert(next.size() == input.size() - 1);
          if (check(next))
          {
            if (g_track)
            {
              for (auto x : input)
                if (is_integer(x))
                  cout << x.numerator() << ' ';
                else
                  cout << x << ' ';
              cout << '\n';
            }
            return true;
          }
          next.clear();
        }
      }
  }
  return false;
}

bool check(int a, int b, int c, int d)
{
  return check(Numbers{a, b, c, d});
}

int main(int argc, char* argv[])
{
  if (argc == 5)
  {
    g_track = true;
    printf("%d\n",
           check(atoi(argv[1]),
                 atoi(argv[2]),
                 atoi(argv[3]),
                 atoi(argv[4])));
  }
  else
  {
    int count = 0;
    int total = 0;
    const int kMax = 10;
    for (int a = 1; a <= kMax; ++a)
      for (int b = a; b <= kMax; ++b)
        for (int c = b; c <= kMax; ++c)
          for (int d = c; d <= kMax; ++d)
          {
            ++total;
            if (check(a, b, c, d))
            {
              printf("%2d %2d %2d %2d\n", a, b, c, d);
              ++count;
            }
          }
    printf("%d %d\n", count, total);
  }
}