45. How to Catch a Thief
class: tweener | impressiveness: 3/5 | factors: requires practice | requires: 3 random objects, collection of small counters | watch full episode
From the genius mind of Martin Gardner, “Gardner’s purloined objects” is a fun logic trick that will allow you to deduce which of your friends has a stolen object in their pocket. This may look a bit overwhelming as you read it, but I promise it’s not nearly as hard as it sounds… plus, it’s way fun to pull off.
The Setup: Grab 3 random friends and 3 random objects (we’ll refer to these random objects as A, B, and C here). Dump out a container of exactly 24 Tic Tacs, matches, or coins (it’s important that you have exactly 24 counters, but it’s equally important that you act like you don’t even know or care how many there are).
Next, pass out a few of the Tic Tacs so one of your players has 1, another has 2, and the last one has 3. From this point forward, think of your “suspects” as #1, #2, and #3, and your “stolen objects” as letters A, B, and C.
Turn your back and ask each of your players to “steal” one object and hide it somewhere you won’t find it.
The Game: Now by giving a few instructions (without looking), you’ll be able to figure out who took which object. While looking away (or blindfolded) give the following instructions to your suspects:
“Whoever took object A: I want you think of how many Tic Tacs you were given… Now take that number out of the pile and eat them.”
“Whoever took object B: I want you think of how many Tic Tacs you were given… Now take TWICE that number out of the pile and eat them.”
“Whoever took object C: I want you think of how many Tic Tacs you were given. Now take FOUR TIMES number out of the pile and eat them.”
When you turn around, there will be some number of Tic Tacs left over (between 1 and 7 of them). This number will reveal to you who has which object, but of course you can’t act like you even care what that number is. Instead, just say “Oh, cool — there’s some left for me!” and eat them all.
Remember, each person has a number of Tic Tacs assigned to them, and each stolen object has a letter assigned to it. So here’s how the number of leftover Tic Tacs gives you the answer of who took what:
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1 Tic Tac: Person 1 has A, 2 has B, 3 has C
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2 Tic Tacs: Person 1 has B, 2 has A, 3 has C
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3 Tic Tacs: Person 1 has A, 2 has C, 3 has B
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4 Tic Tacs: Not possible
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5 Tic Tacs: Person 1 has B, 2 has C, 3 has A
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6 Tic Tacs: Person 1 has C, 2 has A, 3 has B
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7 Tic Tacs: Person 1 has C, 2 has B, 3 has A
…now that’s a lot to keep track of, but luckily, there’s one magic sentence that will make it SUPER easy to remember:
“ABsolutely, BriAn’s ACtive shows BeCkon CheAting ContriButions.”
It’s a silly sentence, but as long as you remember it, you’ll know who has which object. Each word corresponds to a number (1-7), and the capitalized letters tell you, in order, what object person 1 and person 2 have. So if you turn around and there are 3 Tic Tacs left, you’ll look at the third word, “ACtive,” and know that person one has object A, person 2 has C, and (by default,) person 3 has B.
If you turn around and there’s only 1 Tic Tac, then you think of “ABsolutely,” and you’ll know that person 1 has object A, person 2 has object B, and (by default,) person 3 must have object C.
To make this as easy as possible on yourself, make sure to choose 3 objects that are easy to associate with the letters A, B, and C.
Oh, and that magic sentence mnemonic? That came (along with the suggestion for the episode) from Scott Cram, who has sent in several ideas that have turned into some of my favorite episodes of Scam School. Scott runs the Grey Matters blog, a fantastic site dedicated to awesome quirky mathematical and logic puzzles.