While escorting a spider out to the back yard, I mused about how spiders might solve Sudoku puzzles. This is the result. It relates to the party game of Twister patented by Charles F. Foley and Neil W. Rabens in 1966 and originally sold in the United States by Milton Bradley Company.

According to Torsten Sillke, The original inventor, Reyn Guyer, designed a Polka Dot Mat For store display purposes, but later converted it into a game and called it “Pretzel”. Currently, Hasbro Toys which took over Milton Bradley in 1984 sells the game.

I imagine that Spiders “instinctively” solve the puzzle, given the various starting numbers by transitioning from all instances of one value ( such as an 8 ) to all instances of the next value chosen. This is rather unlike humans, who use logic and solve by rows, columns and blocks.

The underlying (!) puzzle is considered hard, but may be made easier by taking the spider’s hints.

This Puzzle uses various sized grids to fit sets of pentominos within. I’ve chosen a 9×9 grid. I think the name, Ripple Effect is suggestive of bigger integers making a bigger splash given their unneighborliness in the rule set. There are no tip sheets as yet, although a strategy may be like that of Paint By Numbers, where you have to account for not only where candidate numbers could be, but also where they cannot be. Ripple Effect was created by Nikoli in 1998.

There are some sites with Ripple Effect Puzzles:

You Play.com, an online puzzle site with free and paid memberships. Getting a free membership is a chore, if not impossible. The form decided my email address was already in use and rejected its association with a new userid! Clicking on Account details made no impression on the script.

Ewe Weidemann’s Sudoku Variants Page.
This site has a huge number of Sudoku and other Puzzle variants well organized, although mostly one example of each kind.

In only a few more years, by December, 21, 2012, that year’s Winter Solstice, the Mayan Calendar (Long Count) will be completed. See “The How And Why Of The Mayan End Date In 2012 A.D.” by John Major Jenkins. It has been keeping track for the last 5125.36 years, since August 11, 3114 B.C. From the accuracy of the Calendar, myths of the end of the world with the end of the calendar have emerged. So the next 5 years will be quite interesting.

The site Mayan Numbers is the reference for Mayan numbers and their names.

Some information about the history of Mayan numbers is given in Mayan Mathematics page

A general introduction to Mayan numerals is located in Mayan Numerals.

It is fascinating to “try on” the various (obscure) number systems and other representations of the digits 1-9 while playing a Sudoku that is not difficult but not easy either.

A (Mensa!) Puzzle Book by Walter Mackay called Repeat-Letter Sudoku caught my eye this week.

This book offers puzzles where there is one (or more) doubled letter(s). In the Cartoon, there are two repeated letters: U and A. No matter. Just do the Sudoku Puzzle as usual and treat each of the pair as two different numbers.

It may help to write the same letters in unique ways: one in block letters and one in cursive or lower case. Alternatively, you can just keep count in every row, column, and block that duplicated letters show up exactly twice.

I like the effect of the no duplicates rule in the original sudoku being relaxed. It forces me to look anew at the puzzle and how it can be done, without prior built up procedural blinders. Interestingly enough, this particular variant appears studiously ignored by the rest of the internet.

I suppose if this carried far enough, it becomes simple to solve (e.g. All but one letter is duplicated 8 times). Don’t do too many of these; you may have to complain to your Eye Doctor that you’re seeing double!

Safe shaking occurs when you envelop the board in loosely wrapped Plastic Wrap. Naturally, the idea is to have the displayed letters (in any orientation) occur in each row, column and block of 9 cells. The cartoon shows a failed attempt. As an added bonus, once you’ve come upon the solution, you can look for small words in the language of your choice occuring contiguously left (backward), or right (forward) or up or down or diagonally.

The game Boggle (TM) was invented by Allan Turoff and usually comes in a 4 x 4 grid. Larger Boggle games use a 5 x 5 grid. There is also a children’s version of Boggle as well as a travel version. See Wikipedia for details.

I’ve gotten some feedback during last week and I am happy to report that the Website for color sudoku puzzles, mentioned last February, 2007, which was called Brainfreeze Puzzles is no longer “frozen”. The site has been revamped; Philip Riley and Laura Taalman’s Color Sudoku book was published in mid-2007.

Look for the Published Puzzles link for free puzzle variations. There are also tutorials for the Sudoku variants. An original innovation is the Bold X variant, with 6 diagonals, 2 main diagonals and 4 “subprime” neighboring diagonals, which have non-repeating digits as well (just not all the numbers).

I’m glad the site is active again. It is a treasure trove of color and variants.

Another viewer simply named Maff, from the United Kingdom, observed that all of the variants that have been shown in this Blog are by and large based on a 9 x 9 Sudoku Grid. This of course is not an accident, since the subtext of the blog is to demonstrate the vast utility of Power (squared) Sudoku White Boards and clipboards, even if (or when) you tire of the original Sudoku puzzle and seek to recapture that old excitement via variations.

Maff has a site called Sudoku Evolution which has created and displays Sudoku variants where the board size is a variable. The site offers a monthly magazine, eBooks, including a free sample pdf file, in which you can modify the file to save or reset your solution entries, as well as print the original puzzle.

The rules for each variant are depicted as graphical animations in an easy and clear manner. Despite there being a few broken links in some of the larger sized 2-D and 3-D puzzles, I plan to spend some time on these kinds of variants. Thanks for letting me know about this site, Maff!

So as I was waiting for my Toyota Matrix (dashboard view) to be serviced, I was reading fairly metaphysical Book called 2012, The Return of Quetzalcoatl, by Daniel Pinchbeck. who spends some time discussing people who take crop circles seriously. Note the cover art.

It occurred to me that because there have been so many instances of crop circle manifestations, especially in the United Kingdom, that the sheer precision and incuse designs would provide clear examples of geometric one-to-one correspondences with the first 9 digits. Clearly, if aliens are trying to communicate with humanity, using geometric art as the communication medium offers a common reality that beats the symbols we use for our number system(s).

I am indebted to Lucy Pringle’s Crop Circle Photographic Library for these images. Her collection of photographs of these mysterious, aerial views of crops bent artistically is extraordinary.

I hope this cartoon helps to publicize her efforts to bring serious attention to all humanity (who’s interested) in this curiously ignored, yet significant messaging system between an unknown entity or entities and humanity.

I wish a happy new year to all, worldwide. Whenever you’re ready.

In the Western World, December is often host to festivals of Light. I’ve adapted a puzzle called Akari or Light Up which was originally invented by Nikoli in 2001. His site provides a tutorial for how the rules of the game interplay. Sample puzzles may be found on Nikoli’s Website, which vary in size from 10 x 10 to 36 x 20.

The puzzle shown in the cartoon is fairly easy to solve. It’s a little reminiscent of the old computer game called Minesweeper. Minesweeper offered adjacency clues which included the boxes diagonal to as well as number of exposed sides. When you incorrectly clear a space that was a mine, a rather startling bang! terminates your game. No sound effects for Akari, however.

The Wikipedia article for Minesweeper has a fascinating discussion about patterns and solving strategies by analyses of single and multiple boxes and mine probabilities. Board difficulty measurements are also detailed.

I came upon Squiggly Sudoku puzzles at Bob Harris’ bumblebeagle.org site. This variant emphasizes the distortion of the 3×3 squares into irregular geometric shapes also containing 9 squares each. His site contains a proof that n-1 starting numbers (or letters) Du-Sum-Oh (Squiggly) exists uniquely for any n x n sized puzzle. The puzzle above has n starting letters for a 9 x 9 sized puzzle, so it should be easier.

Bob Harris offers various sized puzzles on his website and has published a book called Squiggly Sudoku (Sudoku With A Twist) containing 120 various sized puzzles.

He also provides a useful tutorial about how to solve these puzzles. He cites the Big (and Little) Law of Leftovers. The Big Law of Leftovers: Wherever a group of regions overlaps some rows or columns, the parts outside the overlap (the leftovers) have to be the same.

Another pair of authors, Gideon Greenspan and Rachel Lee provide another book of 200 puzzles, also called Squiggly Sudoku However, of these 200, only 144 are Squiggly Sudoku puzzles, the rest are either classic Sudoku (40) or Samarai Sudoku (16) of various levels of difficulty. They also maintain a Website called Web Sudoku with daily (printable) squiggle and other puzzles.

Another Web Site that provide Squiggly Sudokus is Daily Sudoku By Sam Griffiths-Jones. He is also responsible for several sudoku books, including one for kids and an advanced puzzle book. He also sells Electronic Books of puzzles including Squiggly Sudoku puzzles.

This cartoon is comparable to the cartoon I published last June 2, 2007, called Jigsaw Sudoku where numbers instead of letters were used.

While Sudoku puzzle solving is a great boon to maintaining/increasing cognitive brain function, some may eventually get bored with it, hence the invention of Sudoku variants. The fact that boredom sets in to a previously stimulating activity is just human nature. Similarly doing the same physical exercise initially builds muscle tissue but after a while it no longer does.

There is an indication (See Carved in Sand: When Attention Fails and Memory Fades in Midlife by Cathryn Jakobson Ramin, for example) that our brains, when exposed to greater stimulation have a greater number of healthy nerve cells and stronger connections between them. The act of doing puzzles for example, requires continuing novelty to provide sustained stimulation (and interest). The practical consequence of this is to keep our brains agile throughout our entire lives and not have it turn to oatmeal before we’re ready.

Today I am applying the most popular and historically enduring card games using its playing cards to Sudoku. Card Games have been manual endeavors but have tapered off after the 1990s when PCs became sufficiently prevalent. Only since the advent of PCs has digital computer software been written to simulate card games, notably one player Solitaire based games which were a strong motivator of and user interface training, once the PC was available (in offices and homes!).

They are now supplanting physical card games, perhaps most due to the “(double) click” that properly places a card where it should go. This is infinitely more convenient and immeasurably speeds up the game compared with picking up a card and putting it where it belongs. I’m sure some people may “click” on principle just in case the software knows more than they can see (at 3AM).

My favorite visual humor involving Solitaire for the 80s and 90s is shown here.

One way to merge (really small) playing cards with a Sudoku board is to use velcro on all the cards and in each square. Your Sudoku (partial) solutions will persist much longer.

Some interesting Card Game sites include The House of Cards which has information and rules for many kinds of games involving playing cards as well as downloadable software and online versions of card games.

The Card Games Web Site has card and tile games from the world over as well as many links to other card game and card related sites.

Since card games have been around since before 1000 A.D., Where they are believed to have originated in Central Asia and spread to the Moslems and then to Europe and finally to the North and South America and Australia. Look at A Brief History Of Playing Cards” for many fascinating details about the playing card evolution, especially after 1800 in the United States.

The following site also has historical but not necessarily currently played card games: Rules To Period Games

Thanks to all who are following my whimsical Cartoons involving Sudoku variants.

A big thanks to Jim Bumgardner (krazydad.com) for motivating this Cartoon about Slitherlink puzzles. I had not played this before, but it is quite absorbing. His site provides many sets (books) of 16 Slitherlink puzzles in PDF format, along with their unique solution. They are organized according to level of difficulty. In every even numbered book set, the number counts in each puzzle are symmetrically placed, but the solution is definitely always asymmetrical.

In his instructions, he suggests that dot connections that cannot logically occur should be indicated by a thin x so that the remaining possibilities stand out. In the puzzle above, there would be an x between the 3 and the 0, enabling the 3 to be fenced as shown.

Slitherlink is also known as Takegaki along with other names in Wikipedia. The site also provides solution strategies. Another site that has interesting tutorial is the Nikoli puzzle site. Slow motion animated practice always trumps verbal description.

puzzle-loop.com has an FAQ that is very helpful in visualizing what can and cannot be drawn. Puzzles there range from sizes 5×5 to 25×30 in difficulty levels Normal and Hard.

Hirofumi Fujiwara has provided an excellent (non-obvious) “Key to Solution” set of basic, general and strategic rule sets. His site Puzzles And Java World also has puzzles online written in Java including Sudoku, Paint by Numbers, Cross Sums, and Sliding Piece Puzzles.