The best choice is to use a magnet. All you have to do is is get a magnet bar that is about the length of five of your washers (bigger is better). Now just run the magnet over the washers and it will pick them up. Depending on the strength of your magnet, it may take more than one run.
It will look something like this, but with metal washers
You can also make your own electromagnet if you don't have a magnet. Just get a battery, a rubber band, stripped metal wire (see herehere for how to strip metal wire), and a bar of metal maybe a little longer, but thinner, than the magnet I described. Now wrap the wire around the metal bar as many times as you can, but leave a few inches so you attach the wire to the battery. Now put the ends of the wire on the battery and lock them into place with the rubber band. Note: Most batteries will work. The bigger ones are more powerful, but make get hotter faster, so find a good balance. This can get hot so handle with caution. If you are not able to get all the washers up quickly, disconnect the battery and let it cool down. I also recommend working with gloves.
It will look like this, but with a metal bar.