A New Twist on Latin Squares

(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.

Pi Day Sudoku 2009

Remember Pi Day Sudoku 2008?  Well the folk at Brainfreeze Puzzles have done it again!  Here’s their 2009 challenge:

Each row, column, and region contains the digits 1-9 exactly once plus three π symbols.  There’s a printable .pdf file here.

As a bonus, if you send a correct solution in to Brainfreeze puzzles in the next couple months, you’re eligible for a drawing for their book on Color Sudoku!  More details are on their website.

Happy Pi Day Week!

Edited 10/31 to add that the solution hasn’t been posted on the Brainfreeze site yet, but since it’s well past the contest deadline we approved a comment that has the solution (below).

MathFest Sudoku!

The folk at Brainfreeze Puzzles (creator of the famous Pi Day Sudoku) have created a new puzzle for MathFest 2008 in Madison this August!

The official rules are:

Each row, column, and block must contain each digit 1-9 exactly once. Since the middle block is missing, rows and columns that intersect the middle block will have only six visible numbers. In addition, each “Worm” in the puzzle contains numbers that increase from tail to eyes (although not necessarily consecutively). For example, a worm of length four could contain 2, 5, 7, 9 in that order, from tail to eyes.

Sudoku posted with permission. Thanks!

Juxtapositions: Sudoku Lotto

There I was, a mathematician in the grocery checkout line. Inexplicably, I found my eye drawn to the scratch-off lottery ticket machine. Unlike the proverbial punk in a Dirty Harry movie, I did feel lucky, and I surreptitiously slipped a couple bucks out of my wallet, hoping the cashier wouldn’t notice and take me for a fool.

One of the current scratch-off games offered by the New York Lottery is a SuDoKu game.

Juxtapositions: Killer Sudoku

In a comment on an earlier post aboout Sudoku and Kakuro, Batman mentioned a combination of the two games known alternately as Killer Sudoku, Samunamupure or Sum Number Place. As in traditional Sudoku, Killer Sudoku is played on a 9×9 grid in which the digits 1-9 are placed so that each digit appears once in each row, each column, and each 3×3 grid (nonet). As in Kakuro, groups of cells (cages) add to given sums, and within each cage the digits must be distinct.

Sudoku and Kakuro

In recent years many people have played Sudoku, a number game in which a nine-by-nine grid is filled with the digits 1-9 so that each row, each column, and each group of nine squares contains exactly one of each digit.