This week’s puzzle is not about gravity, though you’d be excused for suspecting as much. After all, when most people read “Isaac Newton” and “tree” in the same sentence, they think also of falling apples. But this week’s puzzle, which is widely attributed to Newton, is actually an exercise in orderly arboriculture.
Sunday Puzzles #42: Newton’s Trees
Tree-planting puzzles, which are also known as “points and lines” puzzles, “have always been a matter of great perplexity,” English author and mathematician Henry Ernest Dudeney wrote in in his 1917 collection of puzzles, Amusments in Mathematics. In that text, he refers to Sir Isaac Newton’s tree-planting puzzle, which he calls “the most familiar example” of this genus of brain-teaser. I have restated it briefly, below:
How can nine trees be arranged in ten rows, such that each row contains exactly three trees?
We’ll be back next week with the solution—and a new puzzle! Got a great brainteaser, original or otherwise, that you’d like to see featured? E-mail me with your recommendations. (Be sure to include “Sunday Puzzle” in the subject line.)
SOLUTION to Sunday Puzzle #41: Dueling Cigars
Last week, I described a game in which two players alternate placing cigars on a tabletop. The rules of the game state the last player to to place a cigar on the table wins. The puzzle: Given certain stipulations about the size of the table and the placement of the cigars, one of the players should win every time. Which player is it, and why?
There is a very elegant solution to this puzzle, which many of you identified it in last week’s comments. I believe the first commenter to describe it was DL Thurston. A few minutes later, DarthClem3 and some other comments worked through the solution and arrived at an even more thorough answer over the course of this thread. The solution is this: The secret to winning this game every time is to 1) Be the first player to place a cigar; 2) Place your first cigar at the exact center of the table, standing upright; and 3) Mirror each of player 2’s cigar-placements from thereon out. Gawker Media’s Art Director, Jim Cooke, put together a little animation to help visualize this process: