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Create the magic trick [1] the Intelligent Match Sticks


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I'm starting a genre of puzzles that describes an effect for a magician to present, then asks how would you create the effect. The best answers are the simplest ones. Hidden cameras, tiny mirrors, wireless microphones, one hundred accomplices, quantum transport, infinitely short yellow lines :-) and the like, would not be considered simple methods.

Here's the first puzzle, one described more than 50 years ago by Martin Gardner, which I'm calling the Intelligent Match Sticks.

The effect:

You place three fair dice on a table, in full view of the audience. With your back turned to the table you have a volunteer roll the dice and stack them, three high, in any order and any orientation. You briefly turn and hand him a coin, and have him place it on top of the stack, so that now all the horizontal die faces are obscured.

With your back again turned, the volunteer picks up the dice and adds the numbers from the two touching faces of the top and middle dice. He adds to that sum the numbers from the two touching faces of the middle and bottom dice. Finally he increases the sum by the number on the bottom face of the bottom die. He writes that final sum on a sheet of paper which he folds and puts into his pocket. You then ask him to roll the dice and tell you the total of the three top faces. All this is done out of your sight.

You then turn to the volunteer and hand him some match sticks from your pocket. The number of match sticks equals the number written on the paper.

How is the magician able to hand the volunteer the correct number of match sticks?

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First, we know that adding the numbers on opposite faces of a regular 6-sided die results in 7. So, the total will end up being 21 minus whatever was on the top of the top die.

I'm assuming you can wait and inspect the dice and the coin after turning around (or if the coin gives the info, you are given the coin before turning around).

If the coin is dirty, a little sticky, made of memory foam, or reacts with the face of the die, then you can inspect the coin to find the number of pips that the top of the top die had.

Or perhaps, the coin leaves a smudge on the face of the die that was on top, and you can use that to identify the face that was on top for the number to subtract.

Perhaps the coin is hot/cold and the dice hold temperature for a long time. Then you could touch each face of the dice until you find the hot/cold one.

Any of these good?

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Surely this is a simple misdirection?

The brief turn to hand the coin over is enough, along with the distraction of the introduction of the coin, to glance at the top number on the top die. The totals of the touching numbers on all dice plus the bottom face should be 21 minus the top number, as the opposite faces of a fair die will equal 7. Asking the volunteer to count and add what seem to be random numbers plus the extraneous roll of the dice at the end should be enough to have the audience thinking you've defeated 3 or more random permutations of numbers.

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Surely this is a simple misdirection?

The brief turn to hand the coin over is enough, along with the distraction of the introduction of the coin, to glance at the top number on the top die. The totals of the touching numbers on all dice plus the bottom face should be 21 minus the top number, as the opposite faces of a fair die will equal 7. Asking the volunteer to count and add what seem to be random numbers plus the extraneous roll of the dice at the end should be enough to have the audience thinking you've defeated 3 or more random permutations of numbers.

For some reason I was thinking the magician handed the coin with his back turned. If he could glance the top number while he "briefly turn and hand him a coin," that's all that's needed.

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