Tag: elementary-number-theory

Blog Entry Sunday, June 23, 2024 (c) James Pate Williams, Jr.

The object of this C Win32 application is to find a multiple of 9 with its digits summing to a multiple of 9 also. The first column below is a multiple of 9 whose digits sum to 9 also. The second column is the sum of digits found in the column one number. The last column is the first column divided by 9.

Enter PRNG seed:
1
Enter number of bits (4 to 16):
4
    9       9       1
Enter number of bits (4 to 16):
5
   27       9       3
Enter number of bits (4 to 16):
6
   45       9       5
Enter number of bits (4 to 16):
7
  117       9      13
Enter number of bits (4 to 16):
8
  252       9      28
Enter number of bits (4 to 16):
0

C:\Users\james\source\repos\CProductOf9Console\Debug\CProductOf9Console.exe (process 23280) exited with code 0.
Press any key to close this window . . .
Enter PRNG seed:
1
Enter number of bits (4 to 16):
9
  369      18      41
Enter number of bits (4 to 16):
10
  846      18      94
Enter number of bits (4 to 16):
11
 1080       9     120
Enter number of bits (4 to 16):
12
 3015       9     335
Enter number of bits (4 to 16):
13
 5040       9     560
Enter number of bits (4 to 16):
14
10350       9    1150
Enter number of bits (4 to 16):
15
30870      18    3430
Enter number of bits (4 to 16):
16
57798      36    6422
Enter number of bits (4 to 16):
0
// CProductOf9Console.c (c) Sunday, June 23, 2024
// by James Pate Williams, Jr., BA, BS, MSwE, PhD

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

char nextStr[256], numbStr[256];

void ConvertToString(int number, int radix)
{
	int i = 0;

	while (number > 0)
	{
		nextStr[i++] = (char)(number % radix + '0');
		number /= radix;
	}

	nextStr[i++] = '\0';
	_strrev(nextStr);
}

int Sum(int next)
{
	long sum = 0;

	ConvertToString(next, 10);

	for (int i = 0; i < (int)strlen(nextStr); i++)
		sum += (long)nextStr[i] - '0';

	if (sum % 9 == 0 && sum != 0)
		return sum;

	return -1;
}

long GetNext(int numBits, int* next)
{
	long hi = 0, lo = 0, nine = 0;

	nextStr[0] = '\0';
	numbStr[0] = '\0';

	if (numBits == 4)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 16);

			if (*next != 0 && *next >= 8 && *next < 16)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 5)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 32);

			if (*next >= 16 && *next < 32)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 6)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 64);

			if (*next >= 32 && *next < 64)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 7)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 128);

			if (*next >= 64 && *next < 128)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 8)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 256);

			if (*next >= 128 && *next < 256)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 9)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 512);

			if (*next >= 256 && *next < 512)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 10)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 1024);

			if (*next >= 512 && *next < 1024)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 11)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 2048);

			if (*next >= 1024 && *next < 2048)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 12)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 4096);

			if (*next >= 2048 && *next < 4096)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 13)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 8192);

			if (*next >= 4096 && *next < 8192)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 14)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 16384);

			if (*next >= 8192 && *next < 16384)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 15)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 32768);

			if (*next >= 16384 && *next < 32768)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	else if (numBits == 16)
	{
		while (1)
		{
			*next = 9 * (long)(rand() % 65536);

			if (*next >= 32768 && *next < 65536)
			{
				nine = Sum(*next);

				if (nine % 9 == 0)
					return nine;
			}
		}
	}

	return -1;
}

int main()
{
	char buffer[256] = { '\0' };
	long seed = 0;

	printf_s("Enter PRNG seed:\n");
	scanf_s("%s", buffer, sizeof(buffer));
	seed = atol(buffer);
	srand((unsigned int)seed);

	while (1)
	{
		int next = 0, nine = 0, numberBits = 0;

		printf_s("Enter number of bits (4 to 16):\n");
		scanf_s("%s", buffer, sizeof(buffer));
		numberBits = atol(buffer);

		if (numberBits == 0)
			break;

		if (numberBits < 4 || numberBits > 16)
		{
			printf_s("illegal number of bits must >= 4 and <= 16\n");
			continue;
		}

		nine = GetNext(numberBits, &next);

		if (nine == -1)
		{
			printf_s("illegal result, try again\n");
			continue;
		}

		printf_s("%5ld\t%5ld\t%5ld\n", next, nine, next / 9);
	}

	return 0;
}