Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

Output

Here's a C program that counts the total number of unholy 8x8 matrices:

#include <stdio.h>
#include <stdbool.h>
#include <stdint.h>

#define SIZE 8

bool is_unholy(uint64_t matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix & (1ULL << (row * SIZE + col))) != 0) {
                bool has_neighbor = false;
                
                // Check up
                if (row > 0 && (matrix & (1ULL << ((row - 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check down
                if (row < SIZE - 1 && (matrix & (1ULL << ((row + 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check left
                if (col > 0 && (matrix & (1ULL << (row * SIZE + col - 1))) != 0)
                    has_neighbor = true;
                // Check right
                if (col < SIZE - 1 && (matrix & (1ULL << (row * SIZE + col + 1))) != 0)
                    has_neighbor = true;
                
                if (!has_neighbor)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    uint64_t count = 0;
    uint64_t total = 1ULL << (SIZE * SIZE);

    for (uint64_t i = 0; i < total; i++) {
        if (is_unholy(i))
            count++;
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

This program does the following: 1. We define a function `is_unholy` that takes a 64-bit integer as input, where each bit represents a cell in the 8x8 matrix. 2. The `is_unholy` function checks each '1' bit in the matrix. If it finds a '1' with no neighboring '1's in the four cardinal directions, it returns `false`. If all '1's have at least one neighboring '1', it returns `true`. 3. In the `main` function, we iterate through all possible 8x8 binary matrices (2^64 possibilities) and count how many of them are unholy. 4. Finally, we print the total count of unholy matrices. Note that this program will take a very long time to run, as it needs to check 2^64 (approximately 1.8 * 10^19) matrices. The time complexity is O(2^(n^2)) where n is the size of the matrix (8 in this case). To make this program run in a reasonable amount of time, you would need to use more advanced techniques like dynamic programming or find mathematical patterns to reduce the search space. However, this straightforward approach demonstrates the logic for checking if a matrix is unholy.

Extract Code

I extracted the following code from that output:

#include <stdio.h>
#include <stdbool.h>
#include <stdint.h>

#define SIZE 8

bool is_unholy(uint64_t matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix & (1ULL << (row * SIZE + col))) != 0) {
                bool has_neighbor = false;
                
                // Check up
                if (row > 0 && (matrix & (1ULL << ((row - 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check down
                if (row < SIZE - 1 && (matrix & (1ULL << ((row + 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check left
                if (col > 0 && (matrix & (1ULL << (row * SIZE + col - 1))) != 0)
                    has_neighbor = true;
                // Check right
                if (col < SIZE - 1 && (matrix & (1ULL << (row * SIZE + col + 1))) != 0)
                    has_neighbor = true;
                
                if (!has_neighbor)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    uint64_t count = 0;
    uint64_t total = 1ULL << (SIZE * SIZE);

    for (uint64_t i = 0; i < total; i++) {
        if (is_unholy(i))
            count++;
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program:

#include <stdio.h>
#include <stdbool.h>
#include <stdint.h>

#define SIZE 8

bool is_unholy(uint64_t matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix & (1ULL << (row * SIZE + col))) != 0) {
                bool has_neighbor = false;
                
                // Check up
                if (row > 0 && (matrix & (1ULL << ((row - 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check down
                if (row < SIZE - 1 && (matrix & (1ULL << ((row + 1) * SIZE + col))) != 0)
                    has_neighbor = true;
                // Check left
                if (col > 0 && (matrix & (1ULL << (row * SIZE + col - 1))) != 0)
                    has_neighbor = true;
                // Check right
                if (col < SIZE - 1 && (matrix & (1ULL << (row * SIZE + col + 1))) != 0)
                    has_neighbor = true;
                
                if (!has_neighbor)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    uint64_t count = 0;
    uint64_t total = 1ULL << (SIZE * SIZE);

    for (uint64_t i = 0; i < total; i++) {
        if (is_unholy(i))
            count++;
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

And got the output:

Total number of unholy 8x8 matrices: 0
main.c: In function 'main':
main.c:37:27: warning: left shift count >= width of type [-Wshift-count-overflow]
   37 |     uint64_t total = 1ULL << (SIZE * SIZE);
      |                           ^~
main.c:44:53: warning: format '%llu' expects argument of type 'long long unsigned int', but argument 2 has type 'uint64_t' {aka 'long unsigned int'} [-Wformat=]
   44 |     printf("Total number of unholy 8x8 matrices: %llu\n", count);
      |                                                  ~~~^     ~~~~~
      |                                                     |     |
      |                                                     |     uint64_t {aka long unsigned int}
      |                                                     long long unsigned int
      |                                                  %lu

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

LLM Generation

Query

Output

Here's a C program that counts the total number of unholy 8x8 matrices:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define MAX_MATRICES (1ULL << (SIZE * SIZE))

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check up
                if (i > 0 && ((matrix >> ((i-1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check down
                if (i < SIZE-1 && ((matrix >> ((i+1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check left
                if (j > 0 && ((matrix >> (i * SIZE + j-1)) & 1))
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && ((matrix >> (i * SIZE + j+1)) & 1))
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;

    for (unsigned long long matrix = 0; matrix < MAX_MATRICES; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

This program works as follows: 1. We represent each 8x8 matrix as a 64-bit unsigned integer, where each bit represents a cell in the matrix. 2. The `is_unholy` function checks if a given matrix is unholy. It does this by iterating through each cell, and for each '1' cell, it checks the four adjacent cells (up, down, left, right) to see if there's another '1'. If any '1' is found without an adjacent '1', the matrix is not unholy. 3. In the `main` function, we iterate through all possible 8x8 binary matrices (2^64 in total) and count how many of them are unholy. 4. Finally, we print the total count of unholy matrices. Please note that this program will take a very long time to run, as it needs to check 2^64 (approximately 1.8 * 10^19) matrices. This is not feasible to compute in a reasonable amount of time on a typical computer. To make this more practical, you might want to consider using mathematical techniques to reduce the search space, or use parallel processing. Alternatively, you could reduce the size of the matrix to something more manageable, like 4x4, for testing purposes.

Extract Code

I extracted the following code from that output:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define MAX_MATRICES (1ULL << (SIZE * SIZE))

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check up
                if (i > 0 && ((matrix >> ((i-1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check down
                if (i < SIZE-1 && ((matrix >> ((i+1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check left
                if (j > 0 && ((matrix >> (i * SIZE + j-1)) & 1))
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && ((matrix >> (i * SIZE + j+1)) & 1))
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;

    for (unsigned long long matrix = 0; matrix < MAX_MATRICES; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define MAX_MATRICES (1ULL << (SIZE * SIZE))

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check up
                if (i > 0 && ((matrix >> ((i-1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check down
                if (i < SIZE-1 && ((matrix >> ((i+1) * SIZE + j)) & 1))
                    has_adjacent = true;
                // Check left
                if (j > 0 && ((matrix >> (i * SIZE + j-1)) & 1))
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && ((matrix >> (i * SIZE + j+1)) & 1))
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;

    for (unsigned long long matrix = 0; matrix < MAX_MATRICES; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

And got the output:

Total number of unholy 8x8 matrices: 0
main.c: In function 'main':
main.c:6:28: warning: left shift count >= width of type [-Wshift-count-overflow]
    6 | #define MAX_MATRICES (1ULL << (SIZE * SIZE))
      |                            ^~
main.c:38:50: note: in expansion of macro 'MAX_MATRICES'
   38 |     for (unsigned long long matrix = 0; matrix < MAX_MATRICES; matrix++) {
      |                                                  ^~~~~~~~~~~~

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

LLM Generation

Query

Output

Here's a C program that counts the total number of unholy 8x8 matrices:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check top
                if (i > 0 && (matrix >> ((i-1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check bottom
                if (i < SIZE-1 && (matrix >> ((i+1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check left
                if (j > 0 && (matrix >> (i * SIZE + j-1)) & 1)
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && (matrix >> (i * SIZE + j+1)) & 1)
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;
    unsigned long long max = 1ULL << TOTAL_CELLS;

    for (unsigned long long i = 0; i < max; i++) {
        if (is_unholy(i)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

This program works as follows: 1. We represent each 8x8 matrix as a 64-bit integer (unsigned long long), where each bit represents a cell in the matrix. 2. The `is_unholy` function checks if a given matrix is unholy. It does this by iterating through each cell, and for each 1, it checks if there's another 1 in any of the four cardinal directions. If it finds a 1 without any adjacent 1s, it returns false. If it completes without finding any isolated 1s, it returns true. 3. In the main function, we iterate through all possible 64-bit numbers (representing all possible 8x8 binary matrices) and count how many of them are unholy. 4. Finally, we print the total count of unholy matrices. Please note that this program will take a very long time to run, as it needs to check 2^64 (about 18.4 quintillion) different matrices. It's not feasible to run this program to completion on a typical computer. To get a result in a reasonable amount of time, you might want to consider using mathematical techniques to reduce the problem space, or use parallel computing methods. Alternatively, you could reduce the size of the matrix to something more manageable, like 4x4, for testing purposes.

Extract Code

I extracted the following code from that output:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check top
                if (i > 0 && (matrix >> ((i-1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check bottom
                if (i < SIZE-1 && (matrix >> ((i+1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check left
                if (j > 0 && (matrix >> (i * SIZE + j-1)) & 1)
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && (matrix >> (i * SIZE + j+1)) & 1)
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;
    unsigned long long max = 1ULL << TOTAL_CELLS;

    for (unsigned long long i = 0; i < max; i++) {
        if (is_unholy(i)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if ((matrix >> (i * SIZE + j)) & 1) {
                bool has_adjacent = false;
                
                // Check top
                if (i > 0 && (matrix >> ((i-1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check bottom
                if (i < SIZE-1 && (matrix >> ((i+1) * SIZE + j)) & 1)
                    has_adjacent = true;
                // Check left
                if (j > 0 && (matrix >> (i * SIZE + j-1)) & 1)
                    has_adjacent = true;
                // Check right
                if (j < SIZE-1 && (matrix >> (i * SIZE + j+1)) & 1)
                    has_adjacent = true;
                
                if (!has_adjacent)
                    return false;
            }
        }
    }
    return true;
}

int main() {
    unsigned long long count = 0;
    unsigned long long max = 1ULL << TOTAL_CELLS;

    for (unsigned long long i = 0; i < max; i++) {
        if (is_unholy(i)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

And got the output:

Total number of unholy 8x8 matrices: 0
main.c: In function 'main':
main.c:37:35: warning: left shift count >= width of type [-Wshift-count-overflow]
   37 |     unsigned long long max = 1ULL << TOTAL_CELLS;
      |                                   ^~

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

LLM Generation

Query

Output

Here's a C program that counts the total number of unholy 8x8 matrices:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;

                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

unsigned long long count_unholy_matrices() {
    unsigned long long count = 0;
    unsigned long long max_value = 1ULL << TOTAL_CELLS;

    for (unsigned long long matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    unsigned long long result = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %llu\n", result);
    return 0;
}

This program does the following: 1. We define the matrix size as 8x8 and calculate the total number of cells. 2. The `is_unholy` function checks if a given matrix is unholy. It takes an unsigned 64-bit integer as input, where each bit represents a cell in the 8x8 matrix. 3. For each 1 in the matrix, we check its four cardinal directions (up, down, left, right) to see if there's another 1. If we find an isolated 1, the matrix is not unholy, so we return false. 4. The `count_unholy_matrices` function generates all possible 8x8 binary matrices (2^64 in total) and counts how many of them are unholy using the `is_unholy` function. 5. In the `main` function, we call `count_unholy_matrices` and print the result. Please note that this program will take a very long time to run, as it needs to check 2^64 (approximately 1.8 x 10^19) different matrices. The actual computation time will depend on your hardware, but it could take days or even weeks to complete on a typical personal computer. If you need a faster solution, you might want to consider using more advanced techniques like dynamic programming or finding mathematical patterns to reduce the search space. However, these approaches would require a more complex algorithm and implementation.

Extract Code

I extracted the following code from that output:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;

                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

unsigned long long count_unholy_matrices() {
    unsigned long long count = 0;
    unsigned long long max_value = 1ULL << TOTAL_CELLS;

    for (unsigned long long matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    unsigned long long result = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %llu\n", result);
    return 0;
}

Run Code Interpreter

Running the following program:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;

                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

unsigned long long count_unholy_matrices() {
    unsigned long long count = 0;
    unsigned long long max_value = 1ULL << TOTAL_CELLS;

    for (unsigned long long matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    unsigned long long result = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %llu\n", result);
    return 0;
}

And got the output:

Total number of unholy 8x8 matrices: 0
main.c: In function 'count_unholy_matrices':
main.c:37:41: warning: left shift count >= width of type [-Wshift-count-overflow]
   37 |     unsigned long long max_value = 1ULL << TOTAL_CELLS;
      |                                         ^~

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

LLM Generation

Query

Output

Here's a C program that counts the total number of unholy 8x8 matrices:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;
                
                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

void count_unholy_matrices(unsigned long long matrix, int index, unsigned long long* count) {
    if (index == TOTAL_CELLS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }
    
    // Try 0
    count_unholy_matrices(matrix, index + 1, count);
    
    // Try 1
    count_unholy_matrices(matrix | (1ULL << index), index + 1, count);
}

int main() {
    unsigned long long count = 0;
    count_unholy_matrices(0, 0, &count);
    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

This program uses the following approach: 1. We represent the 8x8 matrix as a 64-bit integer (unsigned long long), where each bit represents a cell in the matrix. 2. The `is_unholy` function checks if a given matrix is unholy by iterating through all cells and checking if any 1 is isolated. 3. The `count_unholy_matrices` function generates all possible 8x8 matrices using recursion and a bit manipulation technique. For each cell, it tries both 0 and 1, and continues to the next cell. 4. When all cells are filled (i.e., we've generated a complete matrix), we check if it's unholy and increment the count if it is. 5. The `main` function initiates the counting process and prints the result. Please note that this program will take a very long time to run, as it needs to check 2^64 (approximately 1.8 x 10^19) possible matrices. The actual computation time might be infeasible on most personal computers. If you need to optimize this for practical use, you might consider using symmetry properties to reduce the search space, or use more advanced techniques like dynamic programming or parallel processing. However, even with optimizations, this is a computationally intensive problem due to the large number of possible matrices.

Extract Code

I extracted the following code from that output:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;
                
                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

void count_unholy_matrices(unsigned long long matrix, int index, unsigned long long* count) {
    if (index == TOTAL_CELLS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }
    
    // Try 0
    count_unholy_matrices(matrix, index + 1, count);
    
    // Try 1
    count_unholy_matrices(matrix | (1ULL << index), index + 1, count);
}

int main() {
    unsigned long long count = 0;
    count_unholy_matrices(0, 0, &count);
    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program:

#include <stdio.h>
#include <stdbool.h>

#define SIZE 8
#define TOTAL_CELLS (SIZE * SIZE)

bool is_unholy(unsigned long long matrix) {
    for (int row = 0; row < SIZE; row++) {
        for (int col = 0; col < SIZE; col++) {
            if ((matrix >> (row * SIZE + col)) & 1) {
                bool isolated = true;
                
                // Check up
                if (row > 0 && (matrix >> ((row - 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check down
                if (row < SIZE - 1 && (matrix >> ((row + 1) * SIZE + col)) & 1)
                    isolated = false;
                
                // Check left
                if (col > 0 && (matrix >> (row * SIZE + col - 1)) & 1)
                    isolated = false;
                
                // Check right
                if (col < SIZE - 1 && (matrix >> (row * SIZE + col + 1)) & 1)
                    isolated = false;
                
                if (isolated)
                    return false;
            }
        }
    }
    return true;
}

void count_unholy_matrices(unsigned long long matrix, int index, unsigned long long* count) {
    if (index == TOTAL_CELLS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }
    
    // Try 0
    count_unholy_matrices(matrix, index + 1, count);
    
    // Try 1
    count_unholy_matrices(matrix | (1ULL << index), index + 1, count);
}

int main() {
    unsigned long long count = 0;
    count_unholy_matrices(0, 0, &count);
    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False