Tell a friend that you will race him in counting from 1 to 100, and
guarantee to win, under the following conditions: You will allow him to
start first, at any number from 1 to 10, and you are both to have the
privilege of adding any figure up to 10 to the last number called. For
instance, we will suppose he starts with 5. You call 15, having mentally
added 10 to his number. He then calls 20, having added 5; and so on,
until 100 is reached. Until he sees through the trick you will win every
time, and even then you will win if you start first and commence at 1.
In that case, as he can only add 10, his first call could not exceed 11,
to which you immediately add 1 and call 12. If his next call is 22, you
say 23. No matter what his additions may be, the numbers you must always
reach first are 12, 23, 34, 45, 56, 67, 78, and 89. When you call the
latter number, as he can only add 10 to it, your next call will, of
course, be 100. By this you will observe that, although you can only add
10 to your opponent's last number, you in reality add 11 to your own. So
you are, so to speak, always 1 ahead of him. If, when you suggest the
trick, you see your friend is not familiar with it, you can give him the
option of starting first, and you need not pick up the thread of your
winning numbers until you reach 50, adding low numbers to his additions,
which will help to puzzle him; but he will soon see that it is necessary
to reach 89; then he will notice you strike 78 and 67. When you see he
is getting on the right track, pick up the winning numbers earlier, and
at last insist that you must now start first. In starting with a person
who does not know the trick it is advisable, and more puzzling, to dodge
about at first and not get on the track of the winning numbers until 56
or 67. But if your friend knows the trick and starts at 1 you cannot
beat him. I have seen good accountants puzzle for hours over this little
trick, which was invented by Mr. William Lawtey, a dear old friend of
mine.