Answer:
The method `puzzle` is a recursive method that takes an integer `num` as input and returns an integer. It adds the value of the input `num` to the result of calling the `puzzle` method recursively with `num/2` as the argument.
To determine the value that will be returned after the following method call `puzzle(5)`, we can work through the steps of the method as follows:
1. The initial value of `num` is 5.
2. Since 5 is greater than 1, the else block is executed.
3. The value of `num` (which is 5) is added to the result of calling `puzzle` recursively with `num/2` (which is 2) as the argument.
4. The value of `num` in the recursive call is now 2.
5. Since 2 is greater than 1, the else block is executed.
6. The value of `num` (which is 2) is added to the result of calling `puzzle` recursively with `num/2` (which is 1) as the argument.
7. The value of `num` in the recursive call is now 1.
8. Since 1 is less than or equal to 1, the if block is executed and the value 1 is returned.
9. The value of the recursive call with `num/2` equal to 1 (which is 1) is added to the current value of `num` (which is 2).
10. The final result is 2+1 = 3.
Therefore, the value that will be returned after the following method call `puzzle(5)` is 3.