Examples of 4 popular mathematical algotihms: fibonacci sequence, factorial (while loop, for loop and recursion), greatest common divisor (while loop and for loop), collatz conjecture (while loop and recursion).
Would you like to see a binary, octal, hexadecimal and roman number versions of your arabic (decimal) number? Check this out!
Program will tell you your date of birth (with day of the week), sex and correctness of your PESEL number. There is a special algotihm for checking correctness of your PESEL number. There are cases where someone has an incorrect PESEL number, for example an incorrect check digit (last digit in your PESEL number). Perhaps after checkin you will have to go to the Citi Hall to change your PESEL number. I hope it won't be necessary. :)
What if it was not in Python language built-in sorted() function? Programmer's live would be more difficult. Example of implementation of 4 most popular sorting algorithms: bubble sort, selection sort, insert sort and quick sort.