Java Puzzles

I’m not that far into my Java journey, but I’ve come across this interesting Java puzzle, set by one of my MSc instructors. I’m setting it down here to help me remember it. The puzzle isn’t unique to our course, and I’ve seen it discussed elsewhere (not that I searched until I’d given it a thorough working over privately, first!).

Essentially, we are asked: “Is the method below to determine whether a number is odd correct?”

public class MyClass {

    public static boolean isOdd(int i) {
        return i % 2 == 1;

    public static void main(String[] args){

        System.out.println("1 is " + isOdd(1));
        System.out.println("2 is " + isOdd(2));    }

isOdd is a predicate function, in that it should return true for odd numbers and false for even numbers. The version you see above, isOdd, has some extra wrapper Java around it–to make it work with Org Babel–, including the two print statements in the main method, but is otherwise identical to the one set by our instructor.

Intuitively, it looks correct. It applies the function modulus 2 (i.e. the remainder when the parameter is divided by two). This should return 0 for even numbers - what we want - and 1 for odd numbers - also what we want.

You can see my testing in the table below.

Table 1: Testing isOdd
Input Modulus Result (% 2) Function Should Output Function Outputs
5 1 True True
4 0 False False
11 1 True True
100 0 False False
-5 1 True False
0 0 False False

Aha - it fails with negative numbers.

This made me double check how a modulus works with negative numbers. It turns out that, in mathematics, the modulus of a negative is normally positive (i.e. without a sign). However, some programming languages - including Java - keep the sign. I can see this is helpful in retaining a something about the calculation. Essentially, it allows us to recover that the one of the terms in the modulus was negative.

And this negative number case is indeed the failure point for the method. To make isOdd work for negatives, our conditional should test for a non-zero remainder such as -1 in the case of modulus 5. The corrected source is below, along with my test numbers from the table above.

public class MyClass {

    public static boolean isOdd(int i) {
        return i % 2 != 0;

    public static void main(String[] args){

        System.out.println("Is 5 odd? " + isOdd(5));
        System.out.println("Is 4 odd? " + isOdd(4));
        System.out.println("Is 11 odd? " + isOdd(11));
        System.out.println("Is 100 odd? " + isOdd(100));
        System.out.println("Is -5 odd? " + isOdd(-5));
        System.out.println("Is 0 odd? " + isOdd(0));
Is 5 odd? true
Is 4 odd? false
Is 11 odd? true
Is 100 odd? false
Is -5 odd? true
Is 0 odd? false
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