Pair magic keyboard with iPad

I cannot pair my new Magic keyboard with my iPad. It shows up in the Bluetooth devices list as "Bluetooth Keyboard", but when I click to connect it I get the message:

Connection Unsuccessful
Make sure "Bluetooth Keyboard" is turned on and in range.

How can I pair the devices?

I went to the Genius Bar to solve this. They did the standard procedure and the device paired.

The explanation for why it was not working for me was that a Magic Keyboard will not pair while it is charging. I had the keyboard plugged into a USB port for charging at the time. To use or pair the keyboard, make sure it is unplugged.

I had the same problem. You can't "swap out batteries" b/c it doesn't have any. Once I paired the keyboard to my computer, it would not re-pair to my iPad...even if I "forget" the keyboard from my computer. Very frustrating that there is no way to force the keyboard into pairing mode.

Solution was to tell the iPad to "Forget" the keyboard too. Then it was able to re-pair.