Chapter: Points and Lines Problems

"Line upon line, line upon line; here a little and there a little." —Isa. xxviii. 10.

What is known as "Points and Lines" puzzles is 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 someday 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.

  1. Problem: The King And The Castles
  2. Problem: Cherries And Plums
  3. Problem: A Plantation Puzzle
  4. Problem: The Twenty-one Trees
  5. Problem: The Ten Coins
  6. Problem: The Twelve Mince-pies
  7. Problem: The Burmese Plantation
  8. Problem: Turks And Russians

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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