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.
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.
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.
I was alerted to this use of the Sudoku Grid in Yahoo! group’s Sudokuworld about a week ago for a completely different variation exercising mental pathways, which for me, are not well traveled. To make the sample puzzle clearer, I used a yellow path that included both endpoints. There will be 9 such yellow paths, (with none that cross each other,) and at least one blank square long so that all the squares are covered by the (unique) solution. Dark lines may also be used to connect like numbers.
My strategy is (“Get It Surrounded”) to start at the outermost Number (i.e. in a corner) and try to connect to its mate. Then work inwards. If the numbers permit, working from right to left, up to down or the reverse also helps. It is a bit irritating that multiple tentative paths are not easily displayed concurrently.
There are puzzle sites with either paired numbers or paired letters. The grids are anywhere from 5×5 to 16×16. In general, the larger the grid, the more difficult the puzzle is to solve.
Sites with Puzzles and/or Tutorials (in English) include:
Nikoli Number Link Puzzles. The tutorial is terse. Nikoli has 3 books published in Japan containing Number Link puzzles exclusively.
Arukone Puzzles. This site is created and maintained by Vegard Hanssen. It has puzzles in 5×5 and 9×9 and is graded for difficulty. The puzzles are printable and solutions can be displayed (but not printed).
Finally, Tim Halbert’s Number Link Site contains an archive of Number Link puzzles (which was generated daily until May 2006). According to Halbert, not all puzzles in the archive have a unique solution. This site also uses the strategy based on working from outside in, to avoid crossed paths. He indicates that Excel can be used as a solving grid, once the numbers are entered. Printing a puzzle out on paper (even multiple times) to solve portably is also a good option.
This Sudoku variant offers the ability of Blocks of 9 to be non-contiguous as well as non-square on the grid. Other versions of this kind of puzzle do not offer the gift of colorization, but merely the outline of the misshapen blocks. This is reminiscent of the Jigsaw Sudoku Puzzle Cartoon of a month ago, which also offered non-square block shapes, but were contiguous. These variants have also been known as Geometric (or Latin Square) Sudoku by Ed Pegg writing for the Mathematical Association of America.
This Sudoku variant supplies the correct triad locations of the numbers of the solved puzzle, but offers far fewer starting numbers. Even so, the puzzle is solvable when considering the subset of candidates that can be in a particular cell.
I found a math site called cut-the-knot.org that shows how you can intersperse only plus or minus signs to the fixed sequence of digits 1 2 3 4 5 6 7 8 9 so that the resulting arithmetic expression, when simplified, is 100. It’s both harder and easier than you think! Likewise, the sequence 9 8 7 6 5 4 3 2 1 is also considered for expressions results simplifying to 100. There’s more than one, but not many.
Jigsaw Sudoku relaxes the requirement of square blocks as in regular Sudoku puzzles. Instead, non-square rectilinear shapes made out of contiguous cells are used instead. The requirement that rows and columns each have unique digits is still true, however.
The abstract describes what may be a fascinating connection between chemistry and color. Unfortunately a paid subscription to the Journal ($45 for US Individual) is required for both the full text of the article and the 3 puzzles and solutions file shown in the article.
Quite free is the Color Sudoku Solver via Excel Spreadsheet by Erkki Hartikainen: downloadable xls file. This spreadsheet solver permits you to map the digits and colors in either direction.
One particularly handy feature is the ability to modify colors depending on your own eyes’ ability to distinguish contrasting colors. The color solver is based on a number Sudoku solver by David Ireland.
The idea for using a string of 81 single digits [the solution] or 81 characters including the blank character [the unsolved puzzle] probably originated on Usenet due to the text based messaging used there. I’ve always been fascinated with Mobius Strips and Klein Bottles (the 3-D analogue). A very enjoyable, math oriented book first published in 1958, Edited by Clifton Fadiman, called Fantasia Mathematica conjectures about the possibilities raised by these strange objects, among other science fiction topics.
Ivars Peterson, written about last week here, has announced his departure from Science News and Math Trek Blog for a position as Director of Publications for Journals and Communications at the Mathematical Association of America (MAA). His new blog, due in March 2007, will be called: The Mathematical Tourist.
Within the MAA Online website, Ed Pegg, back in September 2005, surveyed the varieties of Sudoku and showed many actual variants, some of which are regularly published (especially in Japan). It is an excellent article and a testament to Sudoku puzzlers’ low tolerance for boredom.
I especially like the Cubic Sudoku, which contains 2×4 rectangles on the cube faces with 1×8 “bent in the middle” strips that comprise the “rows” and “columns”. I’m an easy mark for 3-D puzzles.
On a Dutch Web site called Sudokube that I roughly translated with the help of babelfish, there is a hybrid of Sudoku and Rubik’s Cube available for sale for only 7.49 Euros per. (It offers a reduction in price to 5 Euros on its home page.)
This is what I find ironic: the original Rubik’s Cube consisted of 6 colors that get ultimately arranged to have one color per face of the cube. Sudokube has produced a rubik’s-like cube with the digits 1 through 9, in order, on each face, when solved.
Whereas, in my Sudoku Coloring Boards Cartoon of February 10, 2007, I rendered a Sudoku puzzle into a color mapping and a pattern mapping of the digits 1 through 9 from the original starting numbers. I’ve not seen any instances of this variant anywhere else.
I believe this will be very attractive to people whose visual color sense is advanced and whose number sense has been stifled in early life or atrophied. Since I teach math and feel rather un-visual, does anyone else concur (or not) with this?
How do you go about solving the Sudoku Coloring Puzzle as shown in the Cartoon? It seems to me that using small colored dots to make temporary notes in the boxes is analogous to the small numbers one writes as permissible entries. Do you solve the puzzle quicker or slower than one with numbers?
Obviously, solving this is perfect for the Power SudokuČ white board and colored markers found elsewhere on erasablegames.com. If you lack 9 different solid color markers, you can assign patterns for the missing solid colors instead, although that makes small notes harder to write.
The Puzzle is reproduced here and downloadable as a pdf file: