How to do Ctrl+Alt+Del via Logitech iPad keyboard

I think this is a bug in Mac OS X and has something to do with the way the keyboard shortcuts for Spaces are processed. Try this:

• Make sure Spaces is turned on in the System Preferences with the standard 4 spaces layout, and standard key combination for switching to a space.
• Open a folder in the Finder.
• Press and hold CTRL, and press any of the number keys. If you press 5, 6, 7, 8, 9 or 0 first you will get a beep. Same if you press one of those keys again (still holding CTRL). If you then press 1, 2, 3 or 4, you will switch to that space number; or just stay in that space if you were already in it. If you then press any of 5, 6, 7, 8, 9 or 0 again, it won't beep anymore.

If you simply turn off Spaces, the above won't happen and whatever order you press the keys in, they will continue to beep. If you change the number of spaces to only two, then 3, 4, 5, 6, 7, 8, 9 and 0 will give you a beep until you've pressed either 1 or 2. I don't know of an application in which those keys have a non-Spaces functionality and would do something useful other than beep, so I haven't been able to try what happens in such an application. In any case, I don't think you need to worry there's something wrong with your keyboard or the way you've configured the keyboard bindings; it seems to be a bug in Mac OS X.

Edit: Try the above in a new folder in which you've created folders named "1", "2" and so on. I find the Finder's behavior in this case somewhat strange: if you press CTRL-8, it will beep yet also switch the selection to the folder named "8". But again, pressing 5 through 9 will neither beep, nor change the selected folder once you've pressed any of 1 through 4.

Being "cheap Chinese crap" it probably has a generic Bluetooth name like "Bluetooth Keyboard" and maybe has a generic hardware identifier, too. The iPad (or pretty much any computer) can get confused when paired with two different devices that do not distinguish themselves and you might have some conflicting remnant of pairing with another device. So try deleting all the bluetooth parings in your iPad mini and then re-pair this keyboard.