A great deal of fun can be derived from puzzles of this nature--they
are endless in variety--and as they depend upon some principle in
arithmetic should be easily remembered.
Example 1.
Think of a number, say 5
Double it 10
Add 5 15
Add 12 27
Take away 3 24
Halve it 12
Take away number first thought of--5
The answer will _always_ be 7
Example 2.
Think of a number, say 8
Square it 64
Subtract the square of the number which is
1 less than the number thought of--that
is 7--whose square is 49--leaves 15
Add 1 16
When this last number is told, halve it, and you will arrive at
the original number--8.
Example 3.
Think of a number, say 9
Multiply by 3 27
Add 2 29
Multiply by 3 87
Add 2 more than the number thought of (11) 98
The number of _tens_ in the last answer gives the number thought
of, viz., 9.
Example 4.
Think of a number, say 7
Multiply by 3 21
[If product be odd] add 1 22
Halve it 11
Multiply by 3 33
[If product be odd] add 1 34
Halve it 17
Ask how many 9’s are in the remainder, when, of course, the reply
will be 1.
The secret is to bear in mind whether the first sum be odd or even.
If odd first time, retain 1 in the memory; if odd a second time, 2
more, making 3; to which add 4 for every 9 contained in the remainder.
In the above example, there being only one 9 in 17, this gives us 4,
which added to 3 produces the number thought of--7. When even simply
add 4 for every 9 in remainder.