add count unique digits

Author: akgmage

Math/count_unique_digits,go

@@ -0,0 +1,35 @@
+package main
+
+import (
+    "fmt"
+)
+
+func countNumbersWithUniqueDigits(n int) int {
+    // Base case: n = 0, only 1 possible number (0)
+    if n == 0 {
+        return 1
+    }
+    
+    // For n > 0, initialize count to 10 (digits 0-9)
+    count := 10
+    
+    // Calculate count for 2 to n digits
+    for i := 2; i <= n; i++ {
+        // For each number of digits, calculate the number of possible unique numbers
+        // First digit can be 1-9 (9 choices), subsequent digits can be any of the remaining 9-1 = 8 choices
+        // Multiply the choices together to get the total number of possible unique numbers
+        // Add this count to the total count
+        currCount := 9
+        for j := 1; j < i; j++ {
+            currCount *= 10 - j
+        }
+        count += currCount
+    }
+    
+    return count
+}
+
+func main() {
+    // Test case with n = 2
+    fmt.Println(countNumbersWithUniqueDigits(2)) // Output: 91
+}