"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 "luck" is also sometimes of service. Perhaps
some day a genius will discover the key to the whole mystery. Remember
that the trees must be regarded as mere points, for if we were allowed
to make our trees big enough we might easily "fudge" our diagrams and
get in a few extra straight rows that were more apparent than real.
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