Question

PrintStream out = System.out;

    int sum = 0;
    for(int i = 0; i<5; i++)
        for(int j=i; j<5; j++)
            sum++;
    out.println(sum);

outputs: 15. i dont know how this gets 15. i tried solving it in my head, i keep getting 25.

If we ignore the second for loop, and put sum++ in the first for loop, you get 5. But how do we get 15 from the 2nd for loop?

PrintStream out = System.out;

    int sum = 0;
    for(int i = 0; i<5; i++)
        for(int j=i; j<5; j++);
            sum++;
    out.println(sum);

outputs: 1. What happens if you put ; after for statement. does it stop?

Answer 1

i = 0 => j goes from 0 to 4 => sum = 5  
i = 1 => j goes from 1 to 4 => sum = 5 + 4 = 9  
i = 2 => j goes from 2 to 4 => sum = 9 + 3 = 12  
i = 3 => j goes from 3 to 4 => sum = 12 + 2 = 14  
i = 4 => j goes from 4 to 4 => sum = 14 + 1 = 15 

your second code snippet does not compile as it is.

EDIT

Now that your second snippet compiles:

for(int i = 0; i<5; i++)
    for(int j=i; j<5; j++);
        sum++;

is equivalent to (and this is why you should always use braces):

for(int i = 0; i<5; i++) {
    for(int j=i; j<5; j++) {
    }
}
sum++;

That explains why it outputs 1.