# Magic Number Cards

### Some Magical "Guess My Number" Tricks

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This web page gives you a classic "Guess My Number" magic trick, and some variations on it. For each of these tricks, the magician (or is that mathemagician?) asks the subject to think of a number, then shows him or her some cards. For each card, the subject tells the magician whether their number is written on the card. After all the cards are shown, the magician knows the number.

To get a better idea, just watch the video below.

### The original magic number cards

In the classic version of this trick, there are seven cards - you can download a set here. To use them,

• Ask the subject to think of a number from 1 to 100.
• Show them the cards one by one, and ask "Is your number on this card?"
• Whenever the subject says "Yes", note the first number on the card - either 1, 2, 4, 8, 16, 32 or 64.
• Add up all these numbers, and you'll have the subject's secret number.
For example, in the video, my first secret number was 35. It was written on three cards, the first numbers on these cards were 1, 2 and 35. My son worked out 1+2+32 in his head, and found my number, just like magic!

Of course, it's a good idea to practice first, to make sure you've got the idea of the trick - and are confident doing the addition in your head!

There are a couple of ways this trick could go wrong.

• If you make a mistake in your addition, of course you'll end up with the wrong answer. If this happens, just try again, and add more carefully next time!
• Likewise, if the subject says Yes when they should have said No - or the other way around - you won't get their number. If this happens, ask them what their number was, and show them that one of their answers was wrong.
• You might find that your subject already knows the trick! Perhaps they'll say something like "I know this one, it works by binary numbers" or something like that. In that case, try one of the other sets of cards below.
To make the trick more effective,
• Don't tell people the trick! Mathemagicians never tell their secrets! (Ok, I told you, but you're going to be a mathemagician soon, too!)
• Get good at adding up the cards in your head! It might help to memorise a few particular sums : 64+32=96, 64+16=80, 32+16=48.
• Make sure people don't realise you are adding anything up. Be careful not to start muttering "Um, let's see, carry 1, that makes 42, then..."

In the version above, you'll sometimes have to add six of the seven numbers - for example, if the subject picks 63 or 95. I've prepared another set of seven cards where the most addition you'll ever have to do is to add up five numbers.

So,

• Download the cards here, print them out, practise the trick, and try it on your friends!
• Note that the subject's number should still be between 1 and 100. This time, the first numbers of the cards are 1, 2, 4, 8, 15, 28 and 56.

### Up to 1000!

With a set of only 10 magic cards, it's possible to divine any number from 1 to 1000! Of course, the cards are a lot bigger (and the numbers you have to add are a lot bigger too!), but if you're game, you can download and print the set of 10 cards that you need. Then, the trick proceeds as follows...

• Ask the subject to think of a number from 1 to 1000.
• Show them the cards one by one, and ask "Is your number on this card?"
• Add up the first numbers on all the cards they say Yes to (the "first numbers" on the cards are 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512 - but your subject can't say Yes to every card.
• The sum will be their secret number!

### Getting numbers up to 100 with only 5 cards

When I was testing out the first set of magic cards, some people complained there were too many questions to answer. So, I made a new set, with five cards instead of seven - and slightly different rules.

If you download that cards you'll see that the cards have some numbers printed in red, and some in green. Also, the cards are labeled Card 1, Card 3, Card 9, Card 27 and Card 81. The way the trick works is like so :

• Ask the subject to think of a number from 1 to 100.
• Show them the cards one by one, and ask "Is your number on this card? And if so, what color is it?"
• Add up the cards on which their number is Green.
• Add up the cards on which their number is Red.
• Subtract the red total from the green total, and you have their secret number.
For example,
• Suppose I think of the number 69
• Then, I'll tell you my number is Green on Card 81, Red on Card 3 and Card 9, and it doesn't appear on Card 1 or Card 27
• The total for the Green numbers is just 81.
• The total for the Red numbers is 3 + 9, that is, 12.
• So if you work out 81 - 12 you get my secret number 69.
When you're doing this trick, there'll always be some green numbers. If there's no red number, the green total is teh secret number. To see this in action, try (say) 37 as the secret number.

Some tips and tricks for this version of the magic trick :

• The mental math is tougher. Make sure you're confident before trying the trick on your friends!
• In case you don't have a color printer, I've made a black and white set. Each number has either a picture of a Plane (for the numbers you "Plus"), or a Star (for those you Subtract)
• It will be harder for the subject to guess the trick if you cut them so the titles Card 1, Card 3 and so on are not visible. That means you have to remember which card is which, but you'll be able to baffle your friends and family for that much longer!

### And that's all!

Hope you enjoy these magic number card sets!

Yours, Dr Mike...