count_racks.cpp

#include <iostream>

#define PRINT_RACKS 0

static const char NUM_TILES = 27;

int main(int argc, char **argv) {
  char tiles[NUM_TILES][2] = {
    {'A', 9}, {'B', 2}, {'C', 2}, {'D', 4}, {'E', 12}, {'F', 2}, {'G', 3},
    {'H', 2}, {'I', 9}, {'J', 1}, {'K', 1}, {'L', 4}, {'M', 2}, {'N', 6},
    {'O', 8}, {'P', 2}, {'Q', 1}, {'R', 6}, {'S', 4}, {'T', 6}, {'U', 4},
    {'V', 2}, {'W', 2}, {'X', 1}, {'Y', 2}, {'Z', 1}, {'?', 2}
  };
  int num_racks = 0;
  for (int i0 = 0; i0 < NUM_TILES; ++i0) {
    --tiles[i0][1];
    for (int i1 = i0; i1 < NUM_TILES; ++i1) {
      if (tiles[i1][1] == 0) continue;
      --tiles[i1][1];
      for (int i2 = i1; i2 < NUM_TILES; ++i2) {
	if (tiles[i2][1] == 0) continue;
	--tiles[i2][1];
	for (int i3 = i2; i3 < NUM_TILES; ++i3) {
	  if (tiles[i3][1] == 0) continue;
	  --tiles[i3][1];
	  for (int i4 = i3; i4 < NUM_TILES; ++i4) {
	    if (tiles[i4][1] == 0) continue;
	    --tiles[i4][1];
	    for (int i5 = i4; i5 < NUM_TILES; ++i5) {
	      if (tiles[i5][1] == 0) continue;
	      --tiles[i5][1];
	      for (int i6 = i5; i6 < NUM_TILES; ++i6) {
		if (tiles[i6][1] == 0) continue;
#if PRINT_RACKS
		std::cout << tiles[i0][0] << tiles[i1][0] << tiles[i2][0]
			  << tiles[i3][0] << tiles[i4][0] << tiles[i5][0]
			  << tiles[i6][0] << std::endl;
#endif		
		++num_racks;
	      }
	      ++tiles[i5][1];
	    }
	    ++tiles[i4][1];
	  }
	  ++tiles[i3][1];
	}
	++tiles[i2][1];
      }
      ++tiles[i1][1];
    }
    ++tiles[i0][1];
  }
  std::cout << num_racks << std::endl;
  return 0;
}