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Imagine a stack of cards, numbered one to seven in order, with one on the top.
Discard the top card (card 1) and put the next card (card 2) to the bottom of the stack.
Put out card 3 and then put card 4 under.
Continue putting one out and one under until you are holding only one card - it should be card 6.
What happens if you start with 8 cards ?
What happens if you start with 9 cards ?
How much can you find out about this situation ?
Send us whatever you discover.
Continue exploring until you can predict the final card and explain why your method works.