place the number 1
under the central number 13, and the number 2 in the next diagonal
downward. The number 3 should be placed in the same diagonal line; but
as there is no room in the square, you are to place it in that part it
would occupy if another square were placed under this. For the same
reason, the number 4, by following the diagonal direction, falling out
of the square, it is to be put into the part it would hold in another
square, placed by the side of this. You then proceed to numbers 5 and
6, still descending; but as the place 6 should hold is already filled,
you then go back to the diagonal, and consequently place the 6 in the
second place under the 5, so that there may remain an empty space
between the two numbers. The same rule is to observed, whenever you
find a space already filled.

You proceed in this manner to fill all the empty cases in the angle
where the 15 is placed: and as there is no space for the 16 in the
same diagonal, descending, you must place it in the part it would hold
in another square, and continue the same plan till all the spaces are
filled. This method will serve equally for all sorts of arithmetical
progressions composed of odd numbers; even numbers being too
complicated to afford any amusement.

_To find the Difference between two Numbers, the greatest of which is
unknown._

Take as many nines as there are figures in the smallest number, and
subtract that sum from the number of nines. Let another person add
that difference to the largest number, and, taking away the first
figure of the amount, add it to the last figure, and that sum will be
the difference of the two numbers.

For example: Robert, who is 22, tells George, who is older, that he
can discover the difference of their ages; he therefore privately
deducts 22 from 99, and the difference, which is 77, he tells George
to add to his age, and to take away the first figure from the amount,
and add it to the last figure, and that last sum will be the
difference of their ages. Thus, the difference between

Robert's age and 99, is 77
To which George adding his age 35
----
The sum will be 112
----
12
1
----
Then by taking