Question

Given an integer n returns the smallest integer greater than n that does not contain two identical consecutive digits

Answer 1

The function to return the smallest integer greater than n that does not contain two identical consecutive digits can be implemented using the following Python code:

```python

def find_next_number(n):

n += 1

while len(set(str(n))) < len(str(n)):

n += 1

return n

```

This function takes an integer `n` as input, increments it by 1, and iteratively checks if the number contains two identical consecutive digits. If it does, the function continues incrementing until finding the smallest integer greater than `n` that satisfies the condition.

Step-by-step explanation:

The provided Python code defines a function called `find_next_number` that takes an integer `n` as an argument. The function's purpose is to find the smallest integer greater than `n` that does not contain two identical consecutive digits. To achieve this, the code increments the input `n` by 1 and enters a while loop.

Within the loop, the code checks whether the number contains two identical consecutive digits by comparing the length of the set of digits with the length of the string representation of the number. If the condition is not met (i.e., there are no identical consecutive digits), the loop exits, and the function returns the current value of `n`. If the condition is met, indicating the presence of consecutive identical digits, the code increments `n` and continues the process until finding the desired number.

The function ensures that the returned integer is the smallest one greater than the input `n` without containing two identical consecutive digits. The approach involves a systematic search for the appropriate number, guaranteeing the fulfillment of the specified condition.

Answer 2

Certainly! To determine the smallest integer greater than \( n \) that does not contain two identical consecutive digits, you can follow the steps below: 1. Increment the given number \( n \) by 1 to ensure that the new number is greater than \( n \). 2. Convert the new number to a string to inspect its digits easily. 3. Loop through the digits of the number. 4. For each pair of consecutive digits, check whether they are the same. 5. If you find any identical consecutive digits, you'll need to modify the number to remove the repetition. This involves increasing the first digit of the pair and setting all subsequent digits to '0'. After modifying, go back to step 3 to ensure no new repetitions are created. 6. Once the number has no identical consecutive digits, convert the string back to an integer. 7. Return the modified number. Let's go through these steps with an example. Let's say \( n = 2334 \). 1. Increment \( n \) to get 2335. 2. Convert 2335 to a string: "2335". 3. Loop through the digits: - Compare "2" with "3" -> not identical. - Compare the first "3" with the second "3" -> these are identical. 4. Since we found identical consecutive digits "33", increase the first "3" by 1 to get "4", and change the second "3" to "0" to get 2400 (because any digit followed by a "0" is not identical), and proceed back to step 3: - Increment the number to 2401 (to ensure the number is greater than the original n). - Convert to a string: "2401". - Loop through the digits: - Compare "2" with "4" -> not identical. - Compare "4" with "0" -> not identical. - Compare "0" with "1" -> not identical. 5. Since there are no identical consecutive digits, the modification is complete. 6. Convert the string "2401" back to an integer: 2401. 7. Return 2401. So, following this method, the smallest integer greater than 2334 without identical consecutive digits is 2401.