"
Put into one of your hands 5 pieces of money, and desire the person
to tell how many you have got. He will answer 5; upon which open your
hand and show him the 5 pieces. You may then say: "I well knew that
your result was 5; but if you had thought of a very large number, for
example, two or three millions, the result would have been much greater,
but my hand would not have held a number of pieces equal to the
remainder." The person then supposing that the result of the calculation
must be different, according to the difference of the number thought
of, will imagine that it is necessary to know the last number in order
to guess the result; but this idea is false, for, in the case which
we have here supposed, whatever be the number thought of, the remainder
must always be 5. The reason of this is as follows: The sum, the half
of which is given to the poor, is nothing else than twice the number
thought of, plus 10; and when the poor have received their part, there
remains only the number thought of plus 5; but the number thought of
is cut off when the sum borrowed is returned, and consequently there
remains only 5.
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