06 September 2021

Counterintuitive math puzzle

I think the most interesting puzzles are not the ones that are hardest, but the ones that are counterintuitive.  This is a good example:
Your friend choses at random a card from a standard deck of 52 cards, and keeps this card concealed. You have to guess which of the 52 cards it is.

Before you guess, you can ask your friend one of the following three questions:
- is the card red?
- is the card a face card? (Jack, Queen or King)
- is the card the ace of spades?
Your friend will answer truthfully. Which question would you ask that gives you the best chance of guessing the correct card?

Answer below the fold... 

Solution: It doesn’t matter. In all three cases, your chance of guessing the correct card is 1 in 26.
Detailed explanation at The Guardian.  I predict most readers will need to go there to figure this one out.


  1. the first two questions are obvious, as they eliminate half the answers right away. The third took a bit more thought, but I figured it out without going to the site.

  2. “You CAN ask your friend one of the following questions”
    “Which question would you ask that gives you the BEST CHANCE of guessing the correct card?”

    Since it isn’t a requirement (they only say that I CAN, not that I MUST) to ask one of the provided questions, I would just ask my friend what the card was as that would give me the best chance of correctly guessing.


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