This must be stupid question of the day. I have my nRF51822 kit and my nrfGO kit and I can't find the product key. On the box for the nRF51822 there's one tiny sticker with nRF6815, Rev 2.2.0, 2013.44 and 10001989 written on it. None of those appear to be a product key. I've looked at the box it came in, the bags it came with, the invoice, the packing slip, the FedEx invoice, the emailed invoice from Mouser and there is nothing even remotely like a product key.
Where do they hide these things?
