er thought of 4 x 3 = 12 / 2 = 6 x 3 = 18 / 2 = 9.

Here we have one 9, which represents 4, the number thought of.

Number thought of 7 x 3 = 21 + 1 = 22 / 2 = 11 x 3 = 33 + 1 = 34 / 2 =
17. From which is obtainable only one 9, which represents 4, to which
you add 1 for the first addition of 1, and 2 for the second addition,
making a total of 7, the number thought of.

Number thought of,

11
x 3
----
33
+ 1 note 1
----
/ 2 34
17
x 3
----
51
+ 1 note 2
/ 2 52
----
26 two 9's = 8 = 11

HOW TO NAME A NUMBER WHICH HAS BEEN ERASED

Request a member of the company to write a row of figures, the number of
which is immaterial, add them together and subtract the addition from
the row. Then to cross out any figure from the result, add the remaining
figures together and give you the total, when you will tell him which
figure he has erased. Of course, you do not see his figures and can
leave the room while he makes them.

EXAMPLE.

567219 = 30
- 30
--------
567189

We will suppose he crosses out 7, which makes the addition of the row,
minus that figure, 29. He gives you that result and you at once name the
crossed off figure. There are two ways of arriving at the answer. The
simplest and quickest way is to add the units in the result together
until only one figure remains and deduct it from 9. For instance, we
will take 29. Add the 2 and 9 together, which make 11; add 1 and 1
together and you have 2, which deduct from 9, leaving 7, the figure
erased in the above example.

Supposing 1 was the figure erased, the addition of the remaining figures
would then be 35; 3 + 5 = 8, 9 - 8 = 1, the figure crossed off.

The second method is to reckon the next multiple of 9 above the figures
given you; for instance, supposing they are 29, the next multiple of 9
is 36. Deduct 29 from it and it leaves 7, the erased figure. If either 9
or 0 is erased the result is the