Problems with Logitech wireless mouse + keyboard

I recently bought a Logitech wireless keyboard/mouse combo which came with one unifying device. I set it up and they both worked perfectly with a laptop. I then bought a second unifying device to use in my desktop, thinking I could use the same keyboard and mouse.

But I just can't seem to get it to work. I have tried it in the laptop and it works just fine. I read in the logitech setup program notes (I think!) that each unifying unit has to be in a single computer, which makes sense, but when I put one in each computer, one works and one doesn't.

Can you offer some words of wisdom on what i thought originally would be a no-brainer?
RadioGeorgeOwner/ProgrammerAsked:
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Gareth GudgerSolution ArchitectCommented:
Not sure you can pair the same keyboard / mouse with multiple unifying devices. I believe it was the other way round, where you could use multiple keyboards/mice with one unifying device.
Gary CaseRetiredCommented:
The keyboard/mouse can only pair with one receiver (unifying device).

You'll need to buy another keyboard/mouse set with their own receiver.

OR, if you want to use the same keyboard/mouse to control both systems, use a software-based KVM.   Synergy works very nicely for this (and is free):  http://synergy-foss.org/

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