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Card Game (a Simple Version of Clock Patience)

Age 14 to 16 Challenge Level:

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Four cards (two cards with 1 and two with 2) are shuffled and placed into two piles of two

You have two trays labelled 1 and 2.

Starting with the first pile of cards - turn a card over:

  • If the card has a 1 on it - place it in tray 1 and take a card from pile 1
  • If the card has a 2 on it - place it in tray 2 and turn over the next card in pile 2.

You win if all your cards end up in the trays before you run out of cards in one pile.

You lose if there are cards left in a pile that you cannot reach.

What is the probability that you win?

What happens if you have six cards in the two piles (three with one and three with 2)?

Do your odds increase or decrease?

Can you see any patterns in successful and unsuccessful placement of cards in the piles?