A very long card game indeed

Logic Level 2

Consider a row of 1000 playing cards, all face down. You ring up 999 friends and ask them all to come round for a game of cards. The first friend goes along the row of cards and turns over every one. The second friend goes along the row of cards and turns over every second card. The third friend goes along the row of cards and turns over every third card. This repeats for each of your 999 friends. Finally, you go along the row of cards and turn over every 1000th card (i.e. the last card). How many cards are left face up at the end?

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