How do I fill up water balloons?

So I bought a pack of 200 water balloons, but there was no little pump to fill them up with water. My sister said it was strange because they normally provide it, but then again we haven't bought water balloons in a few years.

I can't fill them up from the tap because our tap is a flat one so the balloon nozzle doesn't fit around it. The water just pours out anyway, not expanding the balloon.

I have tried a syringe (without the needle of course) and it is very very hard and took me a very long time to fill up one water balloon. Because I had to fill the syringe, squirt it in the balloon which I had blown up, then I had to hold the balloon nozzle tight so the air wouldn't come out and refill the syringe and so on.

I am also unable to go out and buy a water balloon pump.

Any ideas??

P.S. Water bottles and funnels also dont work...