Question

This is quite literally the first problem in Project Euler. I created these two algorithms to solve it, but they each yield different answers. Basically, the job is to write a program that sums all the products of 3 and 5 that are under 1000.

Here is the correct one:

divisors<-0


for (i in 1:999){
    if ((i %% 3 == 0) || (i %% 5 == 0)){
        divisors <- divisors+i 
        }
    }

The answer it yields is 233168

Here is the wrong one:

divisors<-0

for (i in 1:999){
    if (i %% 3 == 0){
        divisors <- divisors + i
        }
    if (i %% 5 == 0){
        divisors <- divisors + i 
        }
    }

This gives the answer 266333

Can anyone tell me why these two give different answers? The first is correct, and obviously the simpler solution. But I want to know why the second one isn’t correct.

EDIT: fudged the second answer on accident.

Answer 1

Because multiples of 15 will add i once in the first code sample and twice in the second code sample. Multiples of 15 are multiples of both 3 and 5.

To make them functionally identical, the second would have to be something like:

divisors<-0
for (i in 1:999) {
    if (i %% 3 == 0) {
        divisors <- divisors + i
    } else {
        if (i %% 5 == 0) {
            divisors <- divisors + i 
        }
    }
}

But, to be honest, your first sample seems far more logical to me.

As an aside (and moot now that you’ve edited it), I’m also guessing that your second output value of 26633 is a typo. Unless R wraps integers around at some point, I’d expect it to be more than the first example (such as the value 266333 which I get from a similar C program, so I’m assuming you accidentally left of a 3).