//----------------------------------------------------------------------
// enigma1362.c (c) 2005 by Charles Petzold
//
// "Eight-Fifths" by Richard England, New Scientist, 15 October 2005, page 54.
//
// Assume 5 Miles = 8 Kilometers. What the least integral number of 
// miles so rearranging the digits yields the the equivalent integral 
// kilometers?
//
// Let M be miles and K kilometers. The conversion formula is:
//
//	M = (5 / 8) * K
//
// or:
//
//	8 * M = 5 * K
//
// If both M and K are integers, M obviously includes a factor of 5,
// and K includes a factor of 8. Both M and K can be written as these
// factors times a common integer A:
//
//	M = 5 * A
//	K = 8 * A
//
// So, we're looking for an A such that M and K have the same digits 
// but mixed up.
//----------------------------------------------------------------------

#include <stdio.h>

// This function uses an array 'arr[10]' to tally the numbers of each 
// digit that appears in the 'num' argument.
// It conveniently initializes the array to zero as a preliminary.

void TallyDigits(int num, int arr[])
{
	int i;

	for (i = 0; i < 10; i++)
		arr[i] = 0;

	do
	{
		++arr[num % 10];
	}
	while (num /= 10);
}

int main(void)
{
	int M, K, A, i;
	int Mdigits[10], Kdigits[10];

	// Loop through possible A values

	for (A = 1; ; A++)
	{
		// Calculate the miles and kilometers for that value of A

		M = 5 * A;
		K = 8 * A;

		// Tally the digits

		TallyDigits(M, Mdigits);
		TallyDigits(K, Kdigits);

		// Check if the two arrays are the same

		for (i = 0; i < 10; i++)
		{
			if (Mdigits[i] != Kdigits[i])
				break;
		}

		// If so, print the result

		if (i == 10)
		{
			printf("%i Miles = %i Kilometers\n", M, K);
			return 0;
		}
	}
}