Put the ds card write protection slide in the opposite position, you may have made the mistake, happens to e all the time. If you didn't make a mistake the write protection arm in the 3ds sd card slot may be broken. (Hold on... The arm in the ds card must be down to allows access, (this is for safety, although it's almost completely useless, and just annoys my because the slider on my sd card fell off)if the wires disconnected from the arm it can't detect wether or not write protection is on or off, try carefully cleaning the sd card slot), if this doesn't work use any other solutions from the people on the thread, if all else fails send in your ds for repair, try a trusted 3rd party because nintendo charges a lot without warranty.
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This is all from experience when my laptop had the problem, I'm assuming it's pretty close to the same.
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I'm not responsible for your sd breaking because you clean the slot wrong, it's possible to clean it without it breaking, so failure for u to do it right isn't my fault.