Sometimes a seemingly meaningless puzzle makes just enough sense for you to solve it. This is one of those puzzles.
I was recently gifted a book of puzzles in logic and reasoning written by British economist, journalist, and puzzle composer Hubert Phillips. The following puzzle, a brain teaser Phillips calls “Pickled Walnuts,” is one of my favorites from the collection, primarily for its weird wording:
Here is one of those exercises in inference, which so much appealed to Lewis Carroll. You are given a series of statements which may seem to you more or less absurd. But, on the assumption that these statements are factually correct, what conclusion (if any) can be drawn?
- Pickled walnuts are always provided at Professor Piltdown’s parties.
- No animal that does not prefer Beethoven to Mozart ever takes a taxy in Bond Street
- All armadillos can speak the Basque dialect.
- No animal can be registered as a philatelist who does not carry a collapsible umbrella.
- Any animal that can speak Basque is eligible for the Tintinnabulum Club.
- Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
- All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
- The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s.
- Only animals that take taxis in Bond Street carry collapsible umbrellas.
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.)
Last week, I challenged you to figure our how nine trees could be planted in ten straight rows with three trees in every row, a riddle widely attributed to Isaac Newton.
Before we get to the “correct” solution, I wanted to highlight this submission from commenter tuvix. It is not the answer I was looking for (the definition of a “row” of trees, as I see it, is three trees arranged such that a single straight line can be drawn through the center of each tree’s trunk; but tuvix (who gave the correct solution in another comment thread) here uses the word “row” more liberally, defining it as three trees that can have any of their parts, including their outermost foliage, connected by a single straight line), but it is one of the most aesthetically pleasing lateral solutions I’ve seen on Sunday Puzzle:
As for the correct solution, the first person to submit the answer I was looking for was commenter baskev:
baskev’s sketches are pretty rough, but you can tell what they’re going for here. If you’re having a hard time seeing the ten rows of three trees, tuvix actually submitted a cleaner, labeled version of this solution just a few minutes after baskev:
And commenter Campbell Jamieson submitted this alternate solution a few minutes after that:
It seems to me the crux of this puzzle is realizing that different rows need not be equally spaced.
For the mathematically inclined, I recommend this paper on point-line problems and configurations by Harvard mathematician Noam Elkies, in which he discusses methods for resolving point-line problems, and what these can teach us about recent questions in geometry.