NUMB3RS, Part 3: MYSTERY GIFT

by Leigh Lundin

Friends Claire, Judy, and Sharon sent along a magic trick and wondered how it worked. In previous columns (here and here), I revealed the mysteries of a couple of puzzling tricks, so I tackled today’s with interest.

Many similar tricks use mathematical properties, but today’s problem uses nothing beyond fourth grade math. Instead, this trick relies on a little psychology and a lot of magician’s misdirection.

Here, the computer is the magician. She tells you to pick any two-digit number, like choosing two playing cards from a deck. The magician knows the first number (or card) will be 1-9 and the second will be 0-9, but she doesn’t know the specific digits you choose.

The magician tells you to subtract the first and second digits from your original number, and she provides a helpful example 25 – 2 – 5 = 18.

But wait: 22 – 2 – 2 = 18 and 29 – 2 – 9 = 18! What’s going on here?

Let’s say you choose your favorite birthday:

We’ll break this down into separate steps so you can see how it works. We’ll subtract the second digit, which means the magician just made you throw away a card!

Because you have only one card left and it’s in the tens position, we’re left with nothing in the units position– it’s actually a zero, always a zero. The magician now knows you will have either 10, 20, 30, 40, 50, 60, 70, 80, 90, and nothing else.

That’s too easy and you’d catch on what’s happening, so the magician tells you to subtract the first digit from the number. The magician knows the result can be only 9, 18, 27, 36, 45, 54, 63, 72, or 81.

Try any number, and you’ll see what I mean– you’ll always end up with one of these nine numbers. You can verify it here as we do the math:

The magician doesn’t care what numbers you started with because she’s manipulated you into giving her one of nine numbers, while letting you think you’re in control.

Next, the magician shows you 99 boxes and instructs you to identify the gift associated with ‘your’ number (which is no longer yours, but hers). She’s filled all but nine of the boxes with random gift items. The magician makes certain the other nine contain the same gift– that’s right you guessed: box numbers 9, 18, 27, 36, 45, 54, 63, 72, and 81. None of the other ninety boxes matter.

So, upon any given play, all of those nine key boxes will contain the same item– whether it be fruitcake, bunny slippers, or another gift– but the items will be identical in those nine key boxes.

The magician uses one other trick so you don’t become suspicious. You might notice the same items in a diagonal, if the magician listed the items in a 10×10 grid like this:

To obscure how simple the trick is, the magician shows us a 9×11 grid, which makes the pattern more difficult to discern:

Finally, we click NEXT so the magician can reveal her answer:

See? A little psychology, a lot of magical misdirection, and that’s how the trick is done!

Wine, Women, and Mystery

We were shocked to learn there’re other distaff writers beyond our favorite WOMEN OF MYSTERY. If you’re in New York City today, join Ellery Queen‘s editors, writers, and fans an evening of readings by favorite female mystery authors.

Authors Meredith Anthony, SJ Rozan, Sarah Weinman and Elizabeth Zelvin will read excerpts from their EQMM stories at New York City’s KGB Bar.