The eight problems to be solved:

1. Write static recursive function named "sum" that computes and returns the sum of all numbers from 1 to n (where n can be assumed to be is positive) given to the function by means of a parameter.

2. Write static recursive function that finds and returns the smallest element in an integer array, where a reference to the array and the size of the array are provided as parameters.

3. Write static recursive function that computes and returns the sum of the elements in an integer array, where a reference to the array and the size of the array are provided as parameters.

4. Write static recursive function that determines whether or not a string of characters is a palindrome, where a reference to the String is provided as the parameter. Ignore none alphabet characters and ignore case.

5. Write static recursive function that searches a sorted array of integers for a specific integer value using a recursive binary search given parameters

of the array, the starting index of the array, the final index of the array, and the value to be found.

The function returns -1 if the value can't be found or it returns the index of where the value was found in the array.

6. Write static recursive function called letters that takes a lower case letter as its argument and returns a String containing a sequence of letters from 'a' to the given letter. For example: letters('a'); displays "a" and letters('d'); displays "a b c d".

7. Write static recursive function called twos that takes a single integer as its argument and returns the number of factors of 2 in the number. For example: twos (12) should return a 2 and twos (32) a 5.

8.Write static recursive function called powerOf3that takes a single integer as its argument and returns a Boolean value for true if the value is precisely a power of 3 and false if not. For example: powerOf3 (81) should return a true and powerOf3(90) should return a false.