1) Write a program that lets the user type in an integer and produces the Collatz sequence starting with that integer and terminating when the sequence reaches 1. The values of a Collatz sequence are calculated recursively: if the current value in the sequence n is even, the next value is n/2, if n is odd the next value is 3n + 1.

2) Write a simple "guess the number" game. Your program should start by asking the user if they want to play. If they do, the program should select a random integer, ask the user to guess the value, and provide feedback of the form "too high", "too low", or "congratulations" as appropriate. When the correct value is guessed, the user should be offered the opportunity to play again.

3) Write a program to convert an input value from base 10 to a user selectable base between 2 and 16.