rections, but such is the case.

In the accompanying illustration we have two wheels. The lower one is
supposed to be fixed and the upper one running round it in the direction
of the arrows. Now, how many times does the upper wheel turn on its own
axis in making a complete revolution of the other wheel? Do not be in a
hurry with your answer, or you are almost certain to be wrong.
Experiment with two pennies on the table and the correct answer will
surprise you, when you succeed in seeing it.

204.--A NEW MATCH PUZZLE.

[Illustration]

In the illustration eighteen matches are shown arranged so that they
enclose two spaces, one just twice as large as the other. Can you
rearrange them (1) so as to enclose two four-sided spaces, one exactly
three times as large as the other, and (2) so as to enclose two
five-sided spaces, one exactly three times as large as the other? All
the eighteen matches must be fairly used in each case; the two spaces
must be quite detached, and there must be no loose ends or duplicated
matches.

205.--THE SIX SHEEP-PENS.

[Illustration]

Here is a new little puzzle with matches. It will be seen in the
illustration that thirteen matches, representing a farmer's hurdles,
have been so placed that they enclose six sheep-pens all of the same
size. Now, one of these hurdles was stolen, and the farmer wanted still
to enclose six pens of equal size with the remaining twelve. How was he
to do it? All the twelve matches must be fairly used, and there must be
no duplicated matches or loose ends.

POINTS AND LINES PROBLEMS.

"Line upon line, line upon line; here a little and there a
little."--_Isa_. xxviii. 10.

What are known as "Points and Lines" puzzles are found very interesting
by many people. The most familiar example, here given, to plant nine
trees so that they shall form ten straight rows with three trees in
every row, is attributed to Sir Isaac Newton, but the earliest
collection of such puzzles is, I believe, in a rare little book that I
possess--published in 1821--_Rational Amusement for Winter Evenings_, by
John Jackson. The author gives ten examples of "Trees planted in Rows."

These tree-planting puzzles have always been a matter of great
perplexity. They are real "puzzles," in the truest sense of the word,
because nobody has yet succeeded in finding a direct and certain way of
solving them. They demand the exercise of sagacity, ingenuity, and
patience, and what we call