The first therefore is 3, third 13, and the
fourth 17.
When each of the numbers thought of does not exceed 9, they may be
easily found in the following manner:
Having made the person add 1 to the double of the first number thought
of, desire him to multiply the whole by 5, and to add to the product
the second number. If there be a third, make him double this first
sum, and add 1 to it, after which, desire him to multiply the new sum
by 5, and to add to it the third number. If there be a fourth, proceed
in the same manner, desiring him to double the preceding sum; to add
to it 1; to multiply by 5; to add the fourth number; and so on.
Then ask the number arising from the addition of the last number thought
of, and if there were two numbers, subtract 5 from it; if there were
three, 55; if there were four, 555; and so on; for the remainder will
be composed of figures, of which the first on the left will be the
first number thought of, the next second, and so on.
Suppose the numbers thought of be 3, 4, 6; by adding 1 to 6, the double
of the first, we shall have 7, which, being multiplied by 5, will give
35; if 4, the second number thought of, be then added, we shall have
39, which doubled gives 78; and, if we add 1, and multiply 79, the
sum, by 5, the result will be 395.
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