lessons - Playing the game - other draws - challenge 2

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peatterbunut
This might be a stupid question but why can't black king go capture white pawns, to allow black pawns to move up and get promoted? I get why white kind cannot attack as black pawns are in such a way that all of them are protected, but I don't see the automatic draw here... (having trouble wrapping my head around draws and stalemates, just learning about them at the moment). Is it because kings cannot move around aimlessly (which is what white king would be doing)? Thank you!