diff --git a/program4_random.c b/program4_random.c
new file mode 100644
index 0000000..8df7bb4
--- /dev/null
+++ b/program4_random.c
@@ -0,0 +1,285 @@
+#include <stdio.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <time.h>
+
+// 打印数独矩阵
+void printMatrix(int matrix[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        if (i == 0 || i == 3 || i == 6) {
+            printf("|-----------------------|\n");
+        }
+        for (int j = 0; j < 9; j++) {
+            if (j == 0 || j == 3 || j == 6) {
+                printf("| ");
+            }
+            if (matrix[i][j] == 0) {
+                printf(". ");
+            }
+            else {
+                printf("%d ", matrix[i][j]);
+            }
+            if (j == 8) {
+                printf("|\n");
+            }
+        }
+        if (i == 8) {
+            printf("|-----------------------|\n");
+        }
+    }
+}
+
+// 判断数字是否在某行中出现
+int isInRow(int matrix[9][9], int row, int num) {
+    for (int i = 0; i < 9; i++) {
+        if (matrix[row][i] == num) {
+            return 1;
+        }
+    }
+    return 0;
+}
+
+// 判断数字是否在某 3x3 子矩阵中出现
+int isInGroup(int matrix[9][9], int startRow, int startCol, int num) {
+    for (int i = 0; i < 3; i++) {
+        for (int j = 0; j < 3; j++) {
+            if (matrix[startRow + i][startCol + j] == num) {
+                return 1;
+            }
+        }
+    }
+    return 0;
+}
+
+// 判断数字是否在某行中已被使用
+bool usedInRow(int matrix[9][9], int row, int num) {
+    for (int col = 0; col < 9; col++) {
+        if (matrix[row][col] == num) {
+            return true;
+        }
+    }
+    return false;
+}
+
+// 判断数字是否在某列中已被使用
+bool usedInCol(int matrix[9][9], int col, int num) {
+    for (int row = 0; row < 9; row++) {
+        if (matrix[row][col] == num) {
+            return true;
+        }
+    }
+    return false;
+}
+
+// 判断数字是否在某 3x3 子矩阵中已被使用
+bool usedInBox(int matrix[9][9], int boxStartRow, int boxStartCol, int num) {
+    for (int row = 0; row < 3; row++) {
+        for (int col = 0; col < 3; col++) {
+            if (matrix[row + boxStartRow][col + boxStartCol] == num) {
+                return true;
+            }
+        }
+    }
+    return false;
+}
+
+// 判断在特定位置放置特定数字是否安全
+bool isSafe(int matrix[9][9], int row, int col, int num) {
+    return!usedInRow(matrix, row, num) && !usedInCol(matrix, col, num) && !usedInBox(matrix, row - row % 3, col - col % 3, num);
+}
+
+// 查找空位置
+bool findEmptyLocation(int matrix[9][9], int* row, int* col) {
+    for (*row = 0; *row < 9; (*row)++) {
+        for (*col = 0; *col < 9; (*col)++) {
+            if (matrix[*row][*col] == 0) {
+                return true;
+            }
+        }
+    }
+    return false;
+}
+
+// 解决数独问题
+bool solveSudoku(int matrix[9][9]) {
+    int row, col;
+    if (!findEmptyLocation(matrix, &row, &col)) {
+        return true; // 数独已解决
+    }
+    for (int num = 1; num <= 9; num++) {
+        if (isSafe(matrix, row, col, num)) {
+            matrix[row][col] = num;
+            if (solveSudoku(matrix)) {
+                return true;
+            }
+            matrix[row][col] = 0; // 回溯
+        }
+    }
+    return false;
+}
+
+// 检查行是否符合数独规则
+bool checkRows(int matrix[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        int count[9] = { 0 };
+        for (int j = 0; j < 9; j++) {
+            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                int num = matrix[i][j] - 1;
+                if (count[num] > 0) {
+                    return false;
+                }
+                count[num]++;
+            }
+        }
+    }
+    return true;
+}
+
+// 检查列是否符合数独规则
+bool checkColumns(int matrix[9][9]) {
+    for (int j = 0; j < 9; j++) {
+        int count[9] = { 0 };
+        for (int i = 0; i < 9; i++) {
+            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                int num = matrix[i][j] - 1;
+                if (count[num] > 0) {
+                    return false;
+                }
+                count[num]++;
+            }
+        }
+    }
+    return true;
+}
+
+// 检查 3x3 子矩阵是否符合数独规则
+bool checkSubMatrices(int matrix[9][9]) {
+    for (int row = 0; row < 9; row += 3) {
+        for (int col = 0; col < 9; col += 3) {
+            int count[9] = { 0 };
+            for (int i = row; i < row + 3; i++) {
+                for (int j = col; j < col + 3; j++) {
+                    if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                        int num = matrix[i][j] - 1;
+                        if (count[num] > 0) {
+                            return false;
+                        }
+                        count[num]++;
+                    }
+                }
+            }
+        }
+    }
+    return true;
+}
+
+// 判断整个矩阵是否是有效的数独矩阵
+bool isSudokuMatrix(int matrix[9][9]) {
+    return checkRows(matrix) && checkColumns(matrix) && checkSubMatrices(matrix);
+}
+
+int main() {
+    printf("The original Sudoku matrix: \n");
+    srand(time(NULL));
+    int matrix[9][9] = { 0 };
+    int numbers[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
+
+    for (int group = 0; group < 3; group++) {
+        int usedNumbers[9] = { 0 };
+        for (int i = 0; i < 9; i++) {
+            usedNumbers[i] = numbers[i];
+        }
+
+        for (int i = 0; i < 9; i++) {
+            int idx = rand() % (9 - i);
+            int temp = usedNumbers[idx];
+            usedNumbers[idx] = usedNumbers[8 - i];
+            usedNumbers[8 - i] = temp;
+        }
+
+        for (int row = 0; row < 3; row++) {
+            int count = 0;
+            while (count < 3) {
+                int num;
+                do {
+                    int idx = rand() % 9;
+                    num = usedNumbers[idx];
+                } while (num == 0 || isInRow(matrix, group * 3 + row, num) || isInGroup(matrix, group * 3, 0, num));
+
+                int pos;
+                do {
+                    pos = rand() % 9;
+                } while (matrix[group * 3 + row][pos] != 0);
+
+                matrix[group * 3 + row][pos] = num;
+                count++;
+            }
+        }
+    }
+
+    for (int row = 0; row < 9; row++) {
+        int uniqueNumbers[9] = { 0 };
+        int uniqueCount = 0;
+        for (int i = 0; i < 9; i++) {
+            if (matrix[row][i] != 0 && !uniqueNumbers[matrix[row][i] - 1]) {
+                uniqueNumbers[matrix[row][i] - 1] = 1;
+                uniqueCount++;
+            }
+        }
+        if (uniqueCount > 3) {
+            while (uniqueCount > 3) {
+                int idx = rand() % 9;
+                if (matrix[row][idx] != 0 && uniqueNumbers[matrix[row][idx] - 1]) {
+                    matrix[row][idx] = 0;
+                    uniqueCount--;
+                }
+            }
+        }
+        else if (uniqueCount < 3) {
+            while (uniqueCount < 3) {
+                int num;
+                do {
+                    num = rand() % 9 + 1;
+                } while (uniqueNumbers[num - 1]);
+                int idx;
+                do {
+                    idx = rand() % 9;
+                } while (matrix[row][idx] != 0);
+                matrix[row][idx] = num;
+                uniqueNumbers[num - 1] = 1;
+                uniqueCount++;
+            }
+        }
+    }
+
+    printMatrix(matrix);
+    bool valid = isSudokuMatrix(matrix);
+    if (valid) {
+        printf("True:Valid initial Sudoku matrix!\n");
+        if (solveSudoku(matrix)) {
+            printf("The solution of Sudoku matrix:\n");
+            printMatrix(matrix);
+        }
+        else {
+            printf("No solution!\n");
+        }
+    }
+    else {
+        printf("False:Invalid initial Sudoku matrix!\n");
+        for (int j = 0; j < 9; j++) {
+            int count[9] = { 0 };
+            for (int i = 0; i < 9; i++) {
+                if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                    int num = matrix[i][j] - 1;
+                    if (count[num] > 0) {
+                        printf("The number %d in the col %d has been used!\n", matrix[i][j], j);
+                        break;
+                    }
+                    count[num]++;
+                }
+            }
+        }
+        printf("No solution!\n");
+    }
+    return 0;
+}
\ No newline at end of file