Create a class with a method that calls itself to calculate the number of ways a person could climb a staircase of n steps if they can take 1 step at a time, 3 steps at a time, 5 steps at a time, or any combination thereof. Allow the user to specify the number of steps n. Assume at the top of the stairs there is a flat surface so it doesn't matter if the user oversteps on their last step.
Although this problem may seem hard at first think about how you could solve the problem by asking the same problem with one less step on the staircase.
Create a class that has a method to determine if an array entered by the user is a palindrome. This must be done using recursion. A palindrome word is one in which it spells the same things backwards as it does forward.
Create a separate program similar to our example in class with buttons, labels and text fields. This program should hold data for circles. Create an array of circles (a length of 20 should be fine). The user can enter the radius and color of a circle. There should be an add button to add a user entered circle, a modify button to change the radius and/or color of a circle and an average button to find the average radius of all circles. You also should have a set of buttons to navigate through your array of circles, displaying the current one for the user in your text fields.