2 thoughts on “Mathematical card trick

  1. All card names all have a minimum of three letters, so the card in question is in position 7 from the top after the “card” shuffle. The second word is “of”, so the card is now in position 5.

    “Clubs”, “Diamonds”, “Hearts”, and “Spades”. The minimum is 5 letters. Again, the card is guaranteed to be in position 5 after the suit deal. Therefore, it will always be in the fifth position for “Magic”. You can misspell any word (except “of”) and get away with it as long you don’t use fewer letters.

    Given the way each shuffle occurs, the key is 3-2-5. Each number represents the minimum number of cards you need to reorder so that the card is in the fifth position for the pay-off. Anything greater than those numbers has no effect on the card in question.

  2. Here’s a more detailed explanation:

    Here’s the sequence of cards after stacking (numbers represent positions from the top of the deck; #3 is the chosen card): 12X 456 789

    Spelling any word with a minimum of 3 letters will always put the X at position 7 (in the eventuality of words with more than nine letters, the stacking isn’t restarted from the bottom, so we’d just interrupt the spelling once we reach the end of the deck, with all positions reversed). This is guaranteed because no card number names have less than 3 letters). e.g. for “t-h-r-e-e”: 678954X21

    After spelling “o-f”: 8954X2176

    The chosen card (X) is now guaranteed to be at the 5th position from the top. Now we’ll spell the suit name, and all suits (clubs, diamonds, hearts, spades) have at least 5 letters, so the chosen card will be at the 5th position (again). e.g. for “h-e-a-r-t-s”: 1762X4598

    Finally, since “magic” has 5 letters, spelling it will result on X being the last letter picked.

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