Who took what? Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Who took what? Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

For the trick, you need 24 matches, which are stacked next to three small objects, say, a coin, a ring and a key. Three spectators are asked to take part in the focus (we will call them conditionally 1, 2, 3). The first spectator receives one match, the second - two, the third - three. You turn your back on them and ask each of them to take a little thing from those lying on the table (let's call them A, B and C).

Now invite the spectator holding object A to take exactly as many matches from among those left in the pile as he has in his hands. The spectator who took B, let him take twice as many matches as he has in his hands. Ask the last spectator to take object B to take four times as many matches as he has in his hands. After that, have all three spectators put their objects and matches in their pockets.

Turning to the audience and looking at the remaining matches, you immediately tell each spectator what item he took.

Focus secret:

If there is only one match left, then spectators 1, 2, and 3 took objects A, B, and C, respectively (in that order).

If there are 2 matches left, then the order of the items will be B, A, C.

If there are 3 matches left, then A, C, B.

If there are 4 matches, then someone made a mistake, since such a remainder is impossible.

If 5, then the order of the items will be B, C, A.

If 6, then C, A, B.

If 7, then C, B, A.

The mathematical essence of this trick is the fact that the sum 2q + 5r + 1s gets six different values when q, r, s take on the values 2, 3, XNUMX, or some permutation of them.

By the way, coefficients 2, 3, 5 are not the least possible in this trick. It would be possible to use with the same success, for example, coefficients 1, 3, 4 (A does not take matches at all, B takes twice as much as he has in his hands, C - three times as much); in this case, all the sums do not exceed 19, i.e., we can limit ourselves to 19 matches).

A convenient mnemonic would be a list of words whose consonants (in the order in which they are written) correspond to the initial letters of the names of the three selected items. So, for example, if you show a trick with a spoon, fork and knife, then you can offer the following list of words:

1. L and V e N.

2. L e N i V e c.

3. V o L a N.

5. V a N i L.

6. N e V o L i.

7. N a L and V k a.

Here the letter "L" should denote a spoon, "B" - a fork, "H" - a knife. Letters are arranged in words in the order corresponding to the order of objects. The numbers in front of the words indicate the number of matches left.

Author: M.Gardner

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