//---------------------------------------------------------------------------------
// Enigma1341.c (c) 2005 by Charles Petzold (www.charlespetzold.com)
//
// "Two, Three, Four" problem from "New Scientist" magazine, 21 May 2005, page 32.
//
// If letters stand for decimal digits (uniquely), TWO is prime, THREE is 
// triangular, and FOUR is a perfect square. None begin with 0.
//---------------------------------------------------------------------------------

#include <stdio.h>


// Construct a 5-digit number from its five digits
int Number(int i4, int i3, int i2, int i1, int i0)
{
	return 10000 * i4 + 1000 * i3 + 100 * i2 + 10 * i1 + i0;
}

// Returns 1 if argument (> 1) is prime.
int IsPrime(int i)
{
	int j = 2;

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

	return 1;
}

// Returns 1 if argument is triangular
int IsTriangular(int i)
{
	int j = 1;

	while (j * (j + 1) / 2 <= i)
	{
		if (j * (j + 1) / 2 == i)
			return 1;
		j++;
	}

	return 0;
}

// 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;	
}

// Function to prevent multiple letters being the same digit.
// When setting a letter to a digit, pass the letter variable
//	as the first argument and 1 as the second.
//	If 1 is returned, the digit is already used.
// When finished using a digit, pass 0 as the second argument.

int DigitIsUsed(int Digit, int Insert)
{
	static int Digits[10];

	if (Insert && Digits[Digit])
		return 1;

	Digits[Digit] = Insert;
	return 0;
}

int main(void)
{
	int E, F, H, O, R, T, U, W, TWO, THREE, FOUR;

	for (E = 0; E <= 9; E ++)
	{
		DigitIsUsed(E, 1);

		for (F = 1; F <= 9; F++)	// F can't be zero.
		{
			if (DigitIsUsed(F, 1))
				continue;

			for (H = 0; H <= 9; H++)
			{
				if (DigitIsUsed(H, 1))
					continue;

				for (O = 0; O <= 9; O++)
				{
					if (DigitIsUsed(O, 1))
						continue;

					for (R = 0; R <= 9; R++)
					{
						if (DigitIsUsed(R, 1))
							continue;

						for (T = 1; T <= 9; T++)	// T can't be zero
						{
							if (DigitIsUsed(T, 1))
								continue;

							for (U = 0; U <= 9; U++)
							{
								if (DigitIsUsed(U, 1))
									continue;

								for (W = 0; W <= 9; W++)
								{
									if (DigitIsUsed(W, 1))
										continue;

									TWO = Number(0, 0, T, W, O);
									THREE = Number(T, H, R, E, E);
									FOUR = Number(0, F, O, U, R);

									if (IsPrime(TWO) && IsTriangular(THREE) && IsSquare(FOUR))
										printf("TWO = %i, THREE = %i, FOUR = %i\n", TWO, THREE, FOUR);

									DigitIsUsed(W, 0);
								}
								DigitIsUsed(U, 0);
							}
							DigitIsUsed(T, 0);
						}
						DigitIsUsed(R, 0);
					}
					DigitIsUsed(O, 0);
				}
				DigitIsUsed(H, 0);
			}
			DigitIsUsed(F, 0);
		}
		DigitIsUsed(E, 0);
	}
	return 0;
}