Scam School has just released an episode featuring yet another submission from Grey Matters!
Besides showing you the trick, originally published by Martin Gardner in Mathematics Magic and Mystery, I'll teach you an extra tip that wasn't included in the episode!
This trick is called The Purloined Objects:
As Brian says, yes, it was I who came up with the sentence "ABsolutely, BriAn's ACtive shows BeCkon CheAting ContriButions" as a way to help promote his show. In Mathematics Magic and Mystery, Martin Gardner includes other sentences you can use to remember the needed information. Some are for specific objects, such as coins and bills, but he does include some for assorted objects.
How exactly does the trick work? As you might recognize from the use of 1, 2, and 4 as the multiples, the binary system is involved, but we don't even need to delve into the basics of binary in order to explain the workings of the trick.
You might think that 3 people and 3 objects mean that there are 9 possibilities. Actually, since any object chosen means that the others can't choose that object, there are actually only 3 × 2 × 1, or 6 possibilities. Let's take a look at each possibility. As in the video, 1, 2, and 3 will represent the people, and A, B, and C will represent the objects:
1-A 2-B 3-C: 1 takes 1, 2 takes 4, 3 takes 12 = 17 Tic-Tacs taken 1-A 2-C 3-B: 1 takes 1, 2 takes 8, 3 takes 6 = 15 Tic-Tacs taken 1-B 2-A 3-C: 1 takes 2, 2 takes 2, 3 takes 12 = 16 Tic-Tacs taken 1-B 2-C 3-A: 1 takes 2, 2 takes 8, 3 takes 3 = 13 Tic-Tacs taken 1-C 2-A 3-B: 1 takes 4, 2 takes 2, 3 takes 6 = 12 Tic-Tacs taken 1-C 2-B 3-A: 1 takes 4, 2 takes 4, 3 takes 3 = 11 Tic-Tacs taken
In short, each combination of objects, with the rules you give, produces a unique number of objects removed, Therefore, the number of remaining objects codes the arrangement of where the objects were taken! I could take this part of the explanation deeper, but this is enough to understand the trick itself.
Don't forget that you also handed out 6 Tic-Tacs (1 + 2 + 3 = 6) at the beginning, so you actually wind up with a number of objects from 17 (11 + 6) up to 23 (17 + 6). 24 is used in order to give a nice easy code from 1 to 7 when you return. Unfortunately, the different possibilities don't work out in a nice numerical order, so the mnemonic is needed.
Bonus TipHere's an extra tip, first used by the late Stewart James. You may be more familiar with his work than you think. His most famous trick is called Miraskill, which was taught in episode 31 of Scam School as Pigment Prediction.
Perform the trick up to the point where everyone has taken their Tic-Tacs, but you haven't turned around yet. Have a 4th person pick up all the remaining Tic-Tacs, and emphasize to that 4th person that they are to keep them in their hand, and NOT eat them!
Now you turn around, and there seems to be no possible clues that would help you determine anything. You start by divining the number of Tic-Tacs held by that 4th person, and after that, you divine who holds which object! How is this possible?
The answer comes, once again, from Scam School. This time it concerns episode 47, The Coin Trick That Fooled Einstein:
For the 4th person, you divine the number of Tic-Tacs using the principle in the video immediately above. The important point here is to make sure that, in the process of performing this part, you don't forget how many Tic-Tacs the 4th person initially laid down.
After appearing to know how many Tic-Tacs the 4th person had, you continue as in the Purloined Objects video, revealing which person had which object. Notice that this just isn't mixing two tricks together, it also takes the trick to another level by emphasizing your complete lack of information to your audience!
Note: If you're wondering about the title to this post, it's a sort of sequel to the other three posts where Grey Matters was mentioned in Scam School - Scam School Meets Grey Matters, Scam School Meets Grey Matters...Again!, and Scam School Meets Grey Matters...Yet Again!.