//---------------------------------------------------------------------
// enigma1378.c (c) 2006 by Charles Petzold
//
// "Exaudi Deus" by Adrian Somerfield, 
//			New Scientist, 11 February 2006, page 54
//
// Five ascending numbers, all perfect squares less than 1000.
// Each digit that appears occurs exactly three times.
// What's the second number?
//---------------------------------------------------------------------

#include <stdio.h>

int main(void)
{
	int i, n[5];

	// Loop through all combinations of 5 ascending numbers
	// 	whose squares are less than 1000
	for (n[0] =        1; n[0] < 28; n[0]++)
	for (n[1] = n[0] + 1; n[1] < 29; n[1]++)
	for (n[2] = n[1] + 1; n[2] < 30; n[2]++)
	for (n[3] = n[2] + 1; n[3] < 31; n[3]++)
	for (n[4] = n[3] + 1; n[4] < 32; n[4]++)
	{
		int count[10];

		// Zero out the count array
		for (i = 0; i < 10; i++)
			count[i] = 0;

		// Go through 5 numbers
		for (i = 0; i < 5; i++)
		{
			// Calculate the square
			int num = n[i] * n[i];

			// Accumulate the digit counts
			while (num)
			{
				count[num % 10]++;
				num /= 10;
			}
		}

		// Check if each digit appears 0 or 3 times
		for (i = 0; i < 10; i++)
			if (count[i] != 0 && count[i] != 3)
				break;

		// Success if i equals 10
		if (i == 10)
		{
			for (i = 0; i < 5; i++)
				printf("%i ", n[i] * n[i]);

			printf("\n");
		}
	}
	return 0;
}