## A New Twist on Latin Squares

by

(No, it’s not Sudoku.)

After a many-year hiatus, I just re-subscribed to GAMES Magazine, and in my first issue (September 2009), I was pleased to discover several puzzles with a mathematical slant.  One of them was Strimko, a puzzle based on Latin squares, and developed by the Grabarchuk family.  Here’s an example (click to solve online):

The idea is simple: each row and column of an nxn grid must contain the number 1, 2, …, n exactly once (that is, the grid must form a Latin square), and each “stream” (connected path in the grid) must also contain the numbers 1, 2, …, n exactly once.

The official site claims that the minimum number of clues required for an nxn grid is n-1 for n=4, 5, 6, and 7, and also says, “This is another unique feature of Strimko.”  They do not provide a proof, though, so here’s an opportunity for a nice exercise.  (On a related note, a MathSciNet search for “Strimko” returned 0 results, while “latin square” returned 1888 results.  It is left to the reader to determine if there’s anything relevant there.)

There are a few sites that provide weekly (here) or monthly (here, here) puzzle sets.  So in addition to your daily Sudoku fix, maybe a crossword puzzle, and checking your email, you now have yet another way to avoid doing work.

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### 5 Responses to “A New Twist on Latin Squares”

1. Sam Says:

Thanks for this. I discovered Strimko earlier this year, but forgot the name, (Ooops). I knew it had something to do with a river or stream or something.

Thanks again. Brilliant game!

2. watchmath Says:

I solved the example above and take a look another puzzle. The stream in each problem is different, so it is difficult to make a general analysis on this puzzle.

3. Batman Says:

@Sam: Glad you enjoyed it! Judging by the news on their site, I think the GAMES publication was their big break.

@watchmath: For a 4×4 grid, I suppose we could just enumerate the possible stream placements and go from there, but anything bigger would be…daunting. The streams do indeed complicate the problem. But that’s what makes it interesting…right?

4. Peter Grabarchuk Says:

Thank you very much for the great article about our Strimko puzzle concept! We very appreciate it.

Currently we’d like to inform you about unprecedented fact in the puzzling world connected with Strimko. On August 10, 2009, Conceptis Puzzles launched a “new” puzzle concept which they call Chain Sudoku (http://www.conceptispuzzles.com/index.aspx?uri=info/news/315). It’s nothing else than well know Strimko concept which they simply STOLE, and now use without any authorization or licence from its creators – The Grabarchuk Family. I’m sorry to disturb you with this matter, but I thought you must know about this extraordinaire (and quite puzzling) fact.