I found that there may be a problem with pins of the SD card reader but I can't find anything wrong.
The pins on the right touch when the SD card is inserted but not with one on the extreme right. Is this a problem?
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If you think the SD card slot is damaged, then you can attempt a repair (not recommended), or return the Pi to the seller for a new one.
The number of times the LED blinks is indicative as to what the problem could be:
I recommend trying a new SD card just to be certain its not the SD card slot.