# Program to find out the number of special numbers in a given range in Python

Suppose we are given a range of integer numbers and are asked to find out the special numbers in the range. A special number is a number that is a positive integer having only 1 digit in its decimal representation. A number that has more than 1 digit in its decimal representation can also be special if the number is divisible by the count of digits in its decimal representation and the quotient value is itself a special number. We return the count of special numbers in the given range (left_limit, right_limit).

So, if the input is like left_limit = 5, right_limit = 30, then the output will be 13.

The special numbers in this range are: 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 24, and 28.

To solve this, we will follow these steps −

• if right_limit < 10, then
• return right_limit - left_limit + 1
• len_right := size of string representation of (right_limit)
• number_list := [0,1,2,3,4,5,6,7,8,9,10,12,14,16,18]
• for j in range 2 to len_right + 1, do
• for each k in number_list, do
• temp1 := k * j
• if size of string representation of temp1 is same as j, then
• insert temp1 at the end of number_list
• otherwise when len(str(temp1)) > j, then
• come out from the loop
• if number_list[size of number_list - 1] >= right_limit, then
• come out from the loop
• delete duplicate values from number_list and sort
• count := 0
• for each temp2 in number_list, do
• if temp2 >= left_limit and temp2 <= right_limit, then
• count := count + 1
• return count

## Example

Let us see the following implementation to get better understanding −

def strange(left_limit, right_limit):
if right_limit < 10:
return right_limit - left_limit + 1
len_right = len(str(right_limit))
number_list = [0,1,2,3,4,5,6,7,8,9,10,12,14,16,18]
for j in range(2, len_right + 1):
for k in number_list:
temp1 = k*j
if len(str(temp1)) == j:
number_list.append(temp1)
elif len(str(temp1)) > j:
break
if number_list[len(number_list)-1] >= right_limit:
break
number_list = list(set(number_list))
count = 0
for temp2 in number_list:
if temp2 >= left_limit and temp2 <= right_limit:
count = count + 1
return count
print(strange(5, 30))

## Input

5, 30

## Output

13