You probably miss many things but the tablebase does not. 
It's a draw.
Queen vs pawns endgame exercise wants me to win a drawn position
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The last exercise in the queen vs pawns section, where you have to win with the queen against pawns, sometimes starts with a position that is drawn according to the tablebase. Here is an example that I just got:
And analysis board:
This is not the only starting position you can get for that exercise, but I would say roughly 1/4 of the times you get this one. Other positions are winnable.
Am I missing something or is this exercise asking for the impossible?