Will The Cards Match: A Formula

cut cards


Today’s post is for the magic nerds among us. An excellent staple of mental card magic is an effect by Larry Becker called “Will The Cards Match?” It’s based upon a clever math principle first used in magic by Howard Adams, and the trick itself can take many forms depending on the performer’s imagination. My favorite presentation is one that uses a set of business cards: each card has a famous name written on the back, and the cards are torn in half into two mates. After turning all the pieces face down and subjecting them to shuffles, cuts, and a spectator-controlled sorting procedure, the pieces, against all odds, end up paired next to their mates.

Since the standard method of doing this trick uses the spelling of the title phrase, many magicians are curious about 1) What other phrases would also work, and 2) What if instead of using the usual five cards, one wishes to use some other number of cards?

So quite a number of years ago, I worked out a method to determine phrases for any number of cards.  This will allow the performer to customize by occasion and venue the phrase that is used.

Here’s a modified version of how I described it on one of the magic forums about a decade ago:

“A) Suppose each pile of cards contains X cards to begin with. Then a workable phrase could have for its first word X-1 letters, the second word X-2 letters, the third word X-3 letters, the Nth word X-N letters and so on. So, for example, for five cards, four words of lengths 4-3-2-1 will work.

B) But those word lengths are not unique. Each of the word lengths can be adjusted in the following way:

At any point, you may add to any of the above lengths any multiple of the number that is one more than the original word length. That is, at word N, you may add any multiple of X -N+1.

Example: I have two five card piles. By the first formula, I can have a phrase consisting of 4 letters, then 3 letters, then 2 letters, then one letter.

So the first word has length 4—WILL

The second word has length 3—THE

The third word should have length 2—but we’re going to adjust its length for a better phrase.

I can add as many multiples of the original number plus one that I like. Since at this point the original word length would have been 2, I  can add any multiple of three (one more than 2) to the original word length of two.. For instance I can add exactly three to two to get five letters for the third word—CARDS

On the fourth word (on which I originally had 1 letter) I can add any multiple of 2 (one more than one) to my original 1. If I add 2×2 to 1, then I get five—MATCH

So, in this example, I have a phrase consisting of 4-3-5-5 which is Will The Cards Match.

Now let’s try this with six cards in each pile to make this more clear.

To start with:
First word . . . five letters
Second word , . . four letters
Third word . . . three letters
Fourth word . . . Two letters
Fifth word. . . One letter

So a workable sequence of word lengths for 6 cards could be a phrase with 5-4-3-2-1 letters

Now I’ll make some adjustments so that I can get a more convenient phrase:

First word, leave as is . . . five letters—MAGIC.
Second word, leave as is, . . . four letters—WILL.
Third word, originally three letters, which means I can add any multiple of four (one more than three). So I’ll add just 4 to the original three to get seven letters—ASTOUND.
Fourth word, originally two letters, so I can add any multiple of three (one more than two). In this case I’ll add 3 to the original two to get five letters—EVERY.
Fifth word, originally one letter, so I can add any multiple of two (one more than one). In this case, I choose to add two times two to the original one, to get five letters—CHILD.

So my sequence could be 5-4-7-5-5.

For example, “Magic Will Astound Every Child.”

Another sequence that will work using the above instructions is 5-4-3-2-5. Only the last word length needs to be adjusted here. So, “Every Body Can Do Magic.”

It may seem a little complicated, but if you’ll follow along with cards in hand, you’ll see that it works easily, and you can create your own phrase for any number of cards. Let me know if you have any questions.

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