How is the problem in Harry Potter and the Philosopher's Stone solved?

Answer 1

Harry, Ron and Hermione go through the trapdoor to try and save the philosopher's stone. They face a series of challenges which ends in Harry facing off against Professor Quirrell and Lord Voldemort.

In this final room lies the Mirror of Erised which had been enchanted by Albus Dumbledore to protect the stone. Dumbledore's enchantment meant only somebody who wanted to find the stone but not use it, could get it. Therefore the mirror gave Harry the stone. Quirrell tried to take it off him but found he couldn't touch Harry without suffering extreme burns. Harry used this to his advantage in order to hold Quirrell (and therefore Voldemort) off until he passed out, which happened to be when Dumbledore arrived. Quirrell died of his injuries and Voldemort fled.

Dumbledore and his friend, Nicholas Flamel who owned the stone, then agreed it was best to destroy it.