1. Fill in the blanks in the following function definition for adding `a`

to the absolute value of `b`

, without calling `abs`

.

2. Write a function that takes three positive numbers and returns the sum of the squares of the two larger numbers. Use only a single expression for the body of the function:

3. Let’s try to write a function that does the same thing as an if statement:

This function actually doesn’t do the same thing as an if statement in all cases. To prove this fact, write functions c, t, and f such that one of these functions returns the number 1, but the other does not:

4. Douglas Hofstadter’s Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.

Pick a positive number n

If n is even, divide it by 2.

If n is odd, multiply it by 3 and add 1.

Continue this process until n is 1.

The number n will travel up and down but eventually end at 1 (at least for all numbers that have ever been tried — nobody has ever proved that the sequence will always terminate).

The sequence of values of n is often called a Hailstone sequence, because hailstones also travel up and down in the atmosphere before falling to earth. Write a function that takes a single argument with formal parameter name n, prints out the hailstone sequence starting at n, and returns the number of steps in the sequence:

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