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I can download the diagrams to my computer. But can i play them?
As mentioned early on in the page, the file you download to your computer is an SGF file. So you need to install an SGF editor to 'play' them on your computer.
They have at most 10 consecutive moves, so you can replay move-by-move only these. But you can e.g. download a problem and try in an editor. There are quite a lot of editors, I find Drago convenient and it has a nice option to export in the SL ascii format.