1) Write a method that returns a random day of the week ```java String [] days = { "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday" }; int random = (int)(Math.random()*days.length); System.out.println(days[random]); ``` 2) Write a method that accepts an integer as a parameter and returns a String saying if the parameter is odd or even ```java String oddOrEven(int i) { return (i%2 == 0)?"Even":"Odd"; } ``` 3) 1, 2, 4, 8, 16 … are all powers of 2. Print out the first 30 numbers in this sequence. ```java for(int i =0; i<30; i++) { System.out.println(Math.pow(2,i)); } ``` 4) 1, 2, 4, 8, 16 … are all powers of 2. Write a method that checks if a number is a power of 2 and returns true or false ```java boolean powerOfTwo(int i) { //using a bitwise AND... return ((i & (i-1)) == 0) ? true : false; } ``` 5) 1, 8, 27, 81, 243 … are all powers of 3. Write a method that checks if a number is a power of 3 and returns true or false ```java boolean powerOfThree(double d) { while(d >= 3) { d = d/3; } return d == 1; } ``` 6) The first few numbers of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, … Note that the next number in the sequence is the sum of the last two numbers in the sequence. Use a for loop to print out the first 100 fibonacci numbers ```java System.out.print("1, 1, "); int fibp = 1; int fibq = 1; int fib; for(int i = 1; i <29; i++) { fib = fibp + fibq; fibp = fibq; fibq = fib; System.out.print(fib + ", "); } ``` 7) Take a number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process indefinitely. The Collatz Conjecture states that you will always reach 1. Write a method that accepts a number n as input and outputs all the numbers in the sequence, terminating when it reaches 1. ```java void collatz(int i) { while (i != 1) { if (i%2 == 0) { i = i / 2; } else { i = 3*i +1; } System.out.print(i + ", "); } System.out.println(""); } ```