Sometimes a seemingly meaningless puzzle makes just enough sense for you to solve it. This is one of those puzzles.

### Sunday Puzzle #43: Pickled Walnuts

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.)

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### SOLUTION to Sunday Puzzle #42: Newton’s Trees

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:

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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:

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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.

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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.

*Contact the author at rtgonzalez@io9.com. Top photo of pickled walnuts by Amanda Slater | CC BY-SA 2.0.*

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