//-------------------------------------------------------------------
// enigma1347.c (c) 2005 by Charles Petzold (www.charlespetzold.com)
//
// "Fair and Square" from New Scientist, 2 July 2005, page 50.
//
// For a particular word, the "score" is the sum of numeric values for
// each of its letters. 
//
// Begin with A=1, B=2, etc. The problem observes that the score of
// SQUARE (which is 81) is square, PRIME (61) is prime, EVEN (46) is 
// even, and ODD (23) is odd.
//
// Now shuffle the values of three letters. SQUARE is still square, 
// etc, but the scores differ in various ways stated in the problem.
// (See below in the 'for' loops.)
//------------------------------------------------------------------

#include <stdio.h>

// This function calculates a score for a particular string. If the 
// last three arguments are 0, it's the "normal" score for A=1, B=2, etc. 
// Otherwise, the last three arguments indicate the three letters 
// being shuffled. For example, for a shuffling where B=3, C=7, G=2, 
// the arguments are 2, 3, 7.
//
// Because arguments of 3, 7, 2 and 7, 2, 3 produce the same results
// as 2, 3, 7, the convention later on is that i1 is always the lowest 
// number of the three.

int Score(char str[], int i1, int i2, int i3)
{
	int i = 0;
	int scr = 0;	
	char ch;

	while (0 != (ch = str[i++]))
	{
		ch -= 'A';
		
		if (ch == i1)
			ch = i2;

		else if (ch == i2)
			ch = i3;

		else if (ch == i3)
			ch = i1;

		scr += ch + 1;
	}
	return scr;
}

// Returns 1 if argument is prime.

int IsPrime(int i)
{
	int j = 2;

	if (i < 2)
		return 0;

	while (j * j <= i)
	{
		if (i % j == 0)
			return 0;
		j += 1;
	}
	return 1;
}

// Returns 1 if argument is square.

int IsSquare(int i)
{
	int j = 1;

	while (j * j <= i)
	{	
		if (j * j == i)
			return 1;
		j++;
	}
 
	return 0;	
}

// Odd and Even macros.

#define IsOdd(i) ((i) & 1)
#define IsEven(i) (!IsOdd(i))

int main(void)
{
	// These variables store the "normal" scores.

	int scrSQUARE = Score("SQUARE", 0, 0, 0);
	int scrPRIME = Score("PRIME", 0, 0, 0);
	int scrODD = Score("ODD", 0, 0, 0);
	int scrEVEN = Score("EVEN", 0, 0, 0);

	// Shuffled letters are arguments to Score.

	int i1, i2, i3;

	// Notice that i1 is always the lowest, and it can't exceed 'X'.
	// i2 and i3 can go all the way to 'Z'.

	for (i1 = 0;  i1 < 24; i1++)
	for (i2 = i1; i2 < 26; i2++)
	for (i3 = i1; i3 < 26; i3++)
	{
		// Now calculate new scores.

		int newscrSQUARE = Score("SQUARE", i1, i2, i3);
		int newscrPRIME = Score("PRIME", i1, i2, i3);
		int newscrODD = Score("ODD", i1, i2, i3);
		int newscrEVEN = Score("EVEN", i1, i2, i3);

		// Eliminate invalid shufflings.

		if (i2 == i3)
			continue;

		// Problem states new SQUARE score isn't the same as original score.

		if (!IsSquare(newscrSQUARE) || newscrSQUARE == scrSQUARE)
			continue;

		// Problem states new PRIME score is less than original score

		if (!IsPrime(newscrPRIME) || newscrPRIME >= scrPRIME)
			continue;

		if (!IsEven(newscrEVEN) || !IsOdd(newscrODD))
			continue;

		// Problem states at least one of these new scores is different.

		if (newscrEVEN == scrEVEN && newscrODD == scrODD)
			continue;

		// Print the values of the three shuffled letters.

		printf("%c = %i, %c = %i, %c = %i\n", 
		       i1 + 'A', i2 + 1, i2 + 'A', i3 + 1, i3 + 'A', i1 + 1);
	}
	return 0;
}