Ask the sucker to pick
a number but don't say what it is. Tell them
to double it and add some number that you pick (we'll call it
the seed).
The seed can be any even number. Next you tell them to divide
by 2
and subtract the original number that they picked. The answer
will
always be half of the seed. Here's the algebra.
x is their number (don't know,
don't care)
s is the seed that you give.
pick the number x, double it and
add s
= 2 * x + s
divide by 2
= (2 * x + s)/2 = 2x/2 + s/2 =
x + s/2 (at this point they have their number and half of yours)
then subtract the original number
that they picked leaving your seed divided by 2 (hence
the reason the seed needs to be even).
x + s/2 - x = s/2
Example - x is 6 and the seed is
8
(2 * 6 + 8)/2 - 6 = (12 + 8)/2 - 6 = 20/2 - 6 = 10 - 6 = 4 (i.e.,
half of 8)
In the end of course you aren't
guessing their number at all (just half of what you gave them)
but it usually doesn't dawn on them (and of course you never said
that you would guess THEIR number).
This can be extended to any multiplier
such as 3, 4 or 5 etc.. by having them triple, or
quadruple the number and then dividing by 3 or 4 respectively.
The only caveat is that
the seed must be an integral multiple of 3 or 4 etc.
(3x + s)/3 - x = 3x/3 + s/3 - x
= x + s/3 - x = s/3
in general
(Nx + s)/N - x = Nx/N +s/N - x
= x + s/N - x = s/N
As a last extension you can play
this game with any number of people simultaneously by
giving each a different seed, a different multiplier or combinations
of both.
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