Eliminate 1 digit number & construct new number

[MagicNRS]

Hi, recently I saw a street magician performing in public. He started with creating a ‘random’ number (30) in several steps/calculations. That most probably was a forced number using a math formula.

Here are the steps he followed: he asked someone to think of a 1 digit number. Then he showed a card to that person only (so, number 1 to 10) and told him to multiply the number in mind with the shown number. The he says ‘now multiply the result with 4’ and subtract 6 which results in 30.

Question: how does this work? My guess is he eliminates the unknown number in mind and reconstructs 30.

 

[Dr.Peterson]

Hi, recently I saw a street magician performing in public. He started with creating a ‘random’ number (30) in several steps/calculations. That most probably was a forced number using a math formula.

Here are the steps he followed: he asked someone to think of a 1 digit number. Then he showed a card to that person only (so, number 1 to 10) and told him to multiply the number in mind with the shown number. The he says ‘now multiply the result with 4’ and subtract 6 which results in 30.

Question: how does this work? My guess is he eliminates the unknown number in mind and reconstructs 30.

Suppose the 1-digit number is x, and the number on the card is A. Then the constructed number is Ax*4-6 = 30. This implies that Ax = (30+6)/4 = 9.

I don't see that any value of A could force that to happen; in fact, the result could be 30 only if x is a factor of 9, namely 1, 3, or 9. But I can see that, knowing A and the result (here, 30), he could find what x is, namely x = 9/A; or, more generally, if the result is B, then x = (B+6)/(4A). So if the trick were not to force a number, but rather to be able to guess the person's number, then we've got it (and certain choices of A, such as 5, would make the arithmetic easier).

I've seen many versions of this sort of "magic", which generally include a step that cancels out that randomly chosen number (as you suggest). The rest of the trick may also hold a clue as to what he is doing.

[PS: I see you submitted the same question twice, and in the other, you've been given an example of the sort of thing I've seen. The question is, did you state exactly what was done?]

 

[MagicNRS]

Thanks, I came to the same conclusion before posting it. Just saw the reply you mentioned (in the other category). In addition I remember a similar approach using dice. Also the magician could have used a friend to do the math as a ‘random’ person in public.