//-------------------------------------------------------------------------
// enigma1350.c (c) 2005 by Charles Petzold (www.charlespetzold.com)
//
// "All But One" from New Scientist, 23 July 2005, page 47.
//
// Four unique positive digits. All the 4-digit numbers formed by all 24 
// combinations of the digits are summed, then one is subtracted. The 
// result is 122??0. What is the subtracted number?
//-------------------------------------------------------------------------

#include <stdio.h>

int main (void)
{
	int i1, i2, i3, i4;

	// Go through all the combinations of four positive unique
	// digits.  The arrangement of the loops implies that
	// i1 < i2 < i3 < i4, but that doesn't matter because 
	// we're looking at all combinations of these digits.

	for (i1 =      1; i1 <  7; i1++)
	for (i2 = i1 + 1; i2 <  8; i2++)
	for (i3 = i2 + 1; i3 <  9; i3++)
	for (i4 = i3 + 1; i4 < 10; i4++)
	{
		// The sum of all the four-digit numbers formed
		// by all 24 combinations of these digits
		// can be easily calculated. Consider that the
		// least significant digit of the sum contains
		// six i1's plus six i2's plus six i3's plus 
		// six i4's. The other columns are also the 
		// sums of these digits, so:

		int sum = 6666 * (i1 + i2 + i3 + i4);

		// An array containing the four digits:

		int array[] = { i1, i2, i3, i4 };

		// These four integers will index that array:

		int pos1, pos2, pos3, pos4;

		// Loop through the indices.

		for (pos1 = 0; pos1 < 4; pos1++)
		for (pos2 = 0; pos2 < 4; pos2++)
		for (pos3 = 0; pos3 < 4; pos3++)
		for (pos4 = 0; pos4 < 4; pos4++)
		{
			int excnum, x;

			// I hate this code, but...

			if (pos1 == pos2 || pos1 == pos3 || pos1 == pos4 ||
			    pos2 == pos3 || pos2 == pos4 || pos3 == pos4)
				continue;

			// Here's the excluded number. Subtract it from the sum.

			excnum = 1000 * array[pos4] + 100 * array[pos3] + 
					10 * array[pos2] + array[pos1];
			x = sum - excnum;

			// Now see if it fits the pattern 122??0

			if (x / 1000 == 122 && x % 10 == 0)
				printf("Sum = %i\nSum - Excluded = %i\nExcluded = %i\n", 
                                       sum, x, excnum);
		}
	}
	return 0;
}