Wild About Math! Making Math fun and accessible

22Nov/0712

Easy and fun Math trick

4 card Math trickHere's a really easy Math trick you can impress your friends and family with. All you need is 4 index cards and a pen. Here's what you do:

  1. Copy what's on the four cards on the right to your four index cards.
  2. Ask your friend to think of a number between 1 and 15.
  3. Show your friend all 4 cards.
  4. Ask your friend to tell you which cards the number appears in.
  5. Count 1 if he tells you card 1,
    2 if he tells you card 2,
    4 if he tells you card 3, and
    8 if he tells you card 4
  6. Add up the counts.

For example, if your friend thinks of the number 6, then he'll tell you it appears on cards 2 and 3.  Card 2 counts as a 2 and card 3 counts as a 4. Add up the counts, 2+4, and you get 6, the number your friend thought of.

Another example, if your friend thinks of the number 9, then he'll tell you it appears on cards 1 and 4.  Card 1 counts as a 1 and card 4 counts as an 8. Add 1+8 and you get 9.

Can you figure out why this trick works? Hint: It has to do with the binary number system.

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  1. I have these but in different order of numbers and the power of two is in a different corner. I give my classes a Christmas gift every year that they can make. This is perfect for all ages. They can all learn this trick to amaze their families over the holiday break. It’s binary decomposition. Which is why I love it. Great for number sense. They find (or have it confirmed if they are older) that sums of the powers of two can give you any base 10 number you want. You beat me to this post; I was going to put my “magic cards” up in a couple weeks. I’m going to be sure to link to you.

  2. Andree,

    Thanks for writing. I did think about having the numbers in a different order. I left them in order to make it easier for people to find their numbers and to make it easier for kids making the cards to figure out how the trick works.

    I like your website a lot. I stumbled it so maybe other people will discover it.

    Can you recommend any books that have fun little Math explorations like this one? I get lots of inspiration for these posts from books I owned 30 years ago. Often the simple little books are the best.

    Thanks,
    Sol

  3. thank you! that was so nice of you to stumble me! Oh boy, I have so many little books with neat stuff in them (all in storage). I will rumble around and let you know (and post a couple myself).

    I’ve got a new “mission” in life: to try to reach homeschooling parents and public school parents into participating a bit at home with math. so these things are excellent.

  4. Andree,

    Great. I’d love to know about good books of explorations. Thank you.

    I’ve got a similar mission, which you can read about in my “about” page. Helping parents, teachers, home school parents and kids to get excited about Math, especially when it’s simple and accessible, is a great mission. I’m glad to be sharing this mission with you.

  5. I am dyslexic so I learned to do most math in my head in ways that I only recently learned were congruent with higher math laws. I think I saw this on a recent post. I love this trick which I will teach to my grandchildren and to my younger patients. It will be fun to make up a set of cards to demo the trick and a set to give away. Thanks for giving us all this great fun for the holidays.

  6. Hey that’s a cool trick Sol. I won’t even attempt to understand the binary math behind it. Some things are best just left quietly alone, for some of us.

  7. @Fred – More is coming.

    @Bruce – I’d love to dialog with you about how dyslexia affects how you look at Math if you’d be interested in an email dialog for starters.

    @Karen – Glad you enjoyed it.

  8. Cool, that’s a neat trick. So it works as if it were 4 binary lights, and if the number is “in the light” it lights up and you just add the values together… (I think this only makes sense to those who understand binary)

    Cool trick! and yes please give us more!

  9. DJ – yes, you understand it correctly. While it only makes sense to people who understand binary it can also be a good opportunity to teach binary.

    There’s another fun “trick” based on binary that I’ll do a writeup or video on. Stay tuned.

  10. I got my magic card post up finally. I realized suddenly that it’s getting awful close to Christmas break and that I had better prepare! You are linked on the post. Thank you again!

  11. Andree,

    Wonderful post. I like your variation, in particular, the clever way you just have students add up the numbers in the lower left hand corner so that they don’t have to convert numbers to powers of two. And, I really like your extended coverage of what’s going on plus the relationship to the Towers of Hanoi puzzle.

    Very nice.

    Sol


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