//--------------------------------------------------------------------------
// enigma1371.c (c) 2006 by Charles Petzold
//
// "Odd Big Base" by Susan Denham, New Scientist, 17 December 2005, page 52
//
// ODD, BIG, BASE, NAB, and PRIME are all numbers in a base where letters
// continue after the decimal digits. At least two are prime. 
// What is the base?
//
// Well, it's at least 29 (for the 'S') but not more than 36 (when we run
// out of letters.
//--------------------------------------------------------------------------
#include <stdio.h>
#include <string.h>

int ToDecimal(char * pNum, int base)
{
	static char * digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
	char ch;
	int num = 0;

	while ((ch = *pNum++) != 0)
		num = base * num + strchr(digits, ch) - digits;

	return num;
}
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;
}
int main(void)
{
	static char * words[] = { "ODD", "BIG", "BASE", "NAB", "PRIME" };
	int base, i, numprimes;

	for (base = 29; base <= 36; base++)
	{
		for (numprimes = 0, i = 0; i < sizeof(words) / sizeof(words[0]); i++)
			numprimes += IsPrime(ToDecimal(words[i], base));

		if (numprimes > 1)
			printf("Base %i\n", base);
	}
}