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Hidato™ On Sudoku

Hidato On Sudoku

There’s been a significant increase in traffic to this blog ever since I posted the Numbrix puzzle variant at the end of July. For that, I thank you all for visiting.

This week, Barnes and Noble displayed a book by Dr. Gyora Benedek, called Hidato (A Hebrew word meaning: My Puzzle). Dr. Benedek writes an excellent (short) autobiography. The book itself contains variously sized and shaped grids including non-square (and non-quadrilateral) ones. Some web-based 10 x 10 grids have an interesting characteristic in that the middle 4 cells are darkened, indicating that they are not in play, leaving 96 cells to the playing area.

Typically, you’ll be connecting sequence segments based on the starting numbers. Luckily, the connectedness of the overall sequence requires that local neighborhoods of numbers be near in value. What provides a challenge is that It is possible that multiple such sequences may be intermixed.

On the negative side, there’s no facility for saving the current state of the puzzle (without printing it) and when you print the puzzle out, it does not let you return to the puzzle to continue with it.

Have a good time with this variant. This is just the beginning for it.

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Compact Sudoku

Compact Sudoku

A while back, I created a Cartoon called Double Sudoku. In that variant, there were 2 totally separate Sudoku Puzzles embedded in a single Sudoku Grid with all split cells.

The current cartoon is reminiscent of that one, but has N-1 starting numbers that are the same for both puzzles. (Double Sudoku had all different starting numbers for each puzzle.)

In researching where this variant may exist on the internet, I came across a site called, by Dr. Chen, which has generalized this concept even further. Provided are puzzles with as many as 256 possible puzzles generated from multiple “Key Cells” in a single grid.

Normally, a “Key Cell” either contains a single digit M, which signifies that there are that (M) many puzzles bundled together (and you must figure out which digits lead to a solution) or the “Key Cell” contains multiple digits, which means that each of those digits leads to a different Sudoku puzzle.

Truly, this is a “Green” website for Sudoku Puzzles, where the number of Sudoku Grids is severely conserved. His site even offers multiple blank Sudoku grids that may be printed from a pdf or png formatted file.

I’ve provided tips for solving the above puzzle in the single grid by splitting blank cells in two parts. Of course, you can write each puzzle out on paper or duplicate electronically and solve each normally (and one after another).

I hope you enjoy solving this example of Sudoku puzzle cousins twice removed!

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Plain Text Sudoku

Plain Text Sudoku

This cartoon has at its root, a cartoon from 3/4/2007, called Linear Sudoku. For those that wish to describe a Sudoku puzzle to others, particularly by Email, the best way is to create either an 81 character text string or a 9 strings of size 9, where the dot represents the blank cell in both cases.

The site: Sudoku @ Paulspages permits the selection of a Sudoku puzzle, be it random, non-symmetric or from a gallery of puzzles and from that point, it is possible to export it as a text file as shown to the right of the Board in this Cartoon.

There are several benefits for this format, not the least of which is communicating with another puzzler to verify a difficulty or a solution. For those who are visually impaired, they can employ a software program that converts text to speech, thereby permitting the person to hear what the puzzle elements are, so that they can be solved mentally, or transcribed to a braille-writer for reference.

Now that text messaging is becoming most popular, these text strings can convey a puzzle in a minimum of words. This can be useful in timed competitions, where the winning solution is “texted” over to the contest judges for least time and solution correctness. See, for example:
Sudoku Text Challenge sponsored by the TimesOnline and retrieved June 17, 2008.

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Square Root Sudoku

Square Root Sudoku: Disguise The Units Digits, Complete the Puzzle And Be Radical!

I received a wonderful (analog) watch from my niece. It was a Square Root Watch! As a math instructor this made me smile and be pleased with my niece for thinking of me.

The watch is really a low-tech encryption of time, especially for those whose instant reaction to any math-related symbol is anxiety. Look at: if you’d like to acquire a watch like this and also impress your friends. It’s has made everyone laugh who I have showed it to. Of course, the watch wearer may have been the source of amusement. 🙂 hah!

As a result, I adapted this concept to Sudoku puzzling. The result is the cartoon for today. Enjoy the puzzle but don’t be absurd.

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Even Sum Sudoku

Even Sum Sudoku

Today’s puzzle variant comes from the 2008 Sudoku World Competition Instruction booklet. I’ve renamed it Even Sum Sudoku for clarity. About a year ago, I published a cartoon called Odd Sudoku, where either Odd or Even contiguous Cells of at least size 2 were offered. This is not like that.

I’ve eliminated some starting numbers from the original puzzle and identified the cells in yellow as pairs with values summing to an even result.

One question that occurs to me is: what is the probability of having Even Sum Pairs for all the arrangements of this puzzle? Obviously, there are at least 8 Even Sum Pairs that have already been earmarked. From previous calculations (Domino Sudoku Cartoon), excluding the center cell, there are 40 pairs of contiguous cells in an arrangement (and there are 2**4 = 16 pair arrangements since:

  • In Row 1, columns 1 and 2 [A = Across] or the other starting in Column 1, Rows 1. 2 [D = Down]
  • In Row 2, columns 2, 3 [A] or Column 2, Rows 2, 3 [D]
  • In Row 3, columns 3, 4 [A] or Column 3, Rows 3, 4 [D]
  • In Row 4, columns 4, 5 [A] or Column 4, Rows 4, 5 [D]

Since each of these can be selected independently, there are 2*2*2*2 = 16 arrangements.

For any arrangement, how many are Even Pairs are there? It turns out, once you’ve solved the puzzle, you can count:

Across [A]   Down [D]
Odd: 8 Even: 8   Odd: 10 Even: 6
Odd: 9 Even: 3   Odd: 7 Even: 5
Odd: 3 Even: 5   Odd: 5 Even: 3
Odd: 3 Even: 1   Odd: 3 Even: 1
Totals:   Odd: 23 Even: 17   Odd: 25 Even: 15
Arrangement No. Odd Even
AAAA 1 23 17
DDDD 2 25 15
ADAA 3 21 19
AADA 4 25 15
AAAD 5 23 17
DAAA 6 25 15
ADDA 7 23 17
ADAD 8 21 19
AADD 9 25 15
DDAA 10 23 17
DADA 11 27 13
DAAD 12 25 15
ADDD 13 23 17
DADD 14 27 13
DDAD 15 23 17
DDDA 16 25 15
Frequency Odd   Even
2 21   19
6 23   17
6 25   15
2 27   13

P(Even = 19) = .125
P(Even = 17) = .375
P(Even = 15) = .375
P(Even = 13) = .125

A nice discrete, symmetric binomial distribution! Enjoy getting even.

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Hellenic Sudoku

Hellenic Sudoku

Because of the natural correspondence of sequential alphabet lists of letters to positive integers, many non-english alphabets have a strong link to number sequences. The Hellenic (Greek) letters offer a numeric code that can be used to vary Sudoku puzzles.

In reviewing the connotations of this alphabet and its relation to Mathematics (and Statistics), I discovered several interesting sites:

Since I used the Font Face MMa Greek Bold, it automatically translated the number 6 into a right-to-left flipped 3. The original Digamma was more like an F or f. Go figure (so to speak).

This puzzle is considered more than medium difficulty, but if you have become facile in manipulating 9 symbols, the essence of the Sudoku logic should produce a solution sooner than later.

“Wonder is the beginning of wisdom.” — Greek Proverb

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9 Letter Sudoku

9 Letter Sudoku

In reviewing the accumulating collection of Sudoku variants, I noticed that I never offered the “straight-forward” mapping of letters for the digits 1 through 9. I hereby remedy this oversight with this cartoon.

This puzzle is also the outgrowth of a “commission” for me to produce a Sudoku puzzle with special letters spelling out a company name and project acronym. This puzzle is to be used as something to do while listening to how wonderful the future of specific software will be. As always, any feature of the future indicates what is not a feature of the present software. (Once upon a time, this too was future shock and awe.)

This puzzle is rated hard, especially using letters, if you are not used to them. Good luck!

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Superscript Sudoku

Superscript Sudoku

Many Web-based Sudoku puzzle sites offer hints in the form of small sized superscripts (like exponents in Algebra). See my favorite site: Seattle Times Sudoku Page. These superscripts are also known as candidate numbers, which represent the remaining possibilities for values in a cell given the starting numbers (which are normal sized and ordinarily displayed).

It occurred to me that it would be very interesting to throw away the starting numbers and just deal with the superscript hints. Some people create these superscripts in all blank cells as a way to solve the puzzle anyway.

What I did is to initially clarify the proper values from the superscript cell entries to the best that I can determine. Then by looking at the blank cells, I noted that superscript values and totally blank cells contained mutually exclusive values. From that I could deduce the value that must be in a blank cell, based on those superscripts along its row, column and block.

It’s an unusual handicap that provides an enjoyable solution process. Solve on!

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Inverse Sudoku

Inverse Sudoku

Like most interesting games, when turning them around by redefining what loses is now what wins, a fascinating variant can be played. For example, in Chess, if the object is to now be the first player to lose all pieces except the king, and a capture is forced if it is available to be played, this yeilds a variant, called Losing Chess that even novice players can excel at.

Another game is called Losing Checkers where you play Checkers according to normal rules (forced to capture if the opportunity arises) but the Loser wins.

In this spirit, I thaought about what it might mean for Sudoku puzzle solving. Since there are so many ways you can fail to solve a puzzle, this didn’t seem to challenging 🙂

In this Cartoon variant, We start with a Sudoku solved puzzle and proceed to erase numbers until we have an incomplete or starting puzzle (depending on when you stop erasing). Then try to solve the puzzle that is presented.

If you don’t erase enough numbers, the puzzle may be easily solved. If you erase just enough numbers, (in this case 53 of them), you may either have a uniquely solvable puzzle with a single solution or you may have one with more than one solution. If you keep removing more than 53 numbers (in this case), your ultimate solution may have multiple answers. This means that your starting numbers are “ambiguous”.

There are many programmatic aids in solving sudoku puzzles on the internet, both web based and downloadable applications. One category are Sudoku Puzzle Generators where they produce the starting numbers and you solve. There are also Sudoku Solver Sites, many of which have user interfaces so that *their* puzzle may be solved by you online.

The trick is to find Sudoku Solvers where you get to input the starting numbers. Some sites I found offer:

(1) Excel based Sudoku all in one Generator and Solver by Hari Kumar

(2) Excel based Sudoku-xls Generator, Workpad and Solver by Peter Mladek

(3) AT&T Research Command line: A 9 x 9 Sudoku Solver And Generator And Starting Number analysis

(4) GNUDoQ 0.94 Sudoku Solver

(5) David Ireland’s Number Sudoku Solver (Excel Based)

Happy Erasing!

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Kanji Sudoku

Kanji Sudoku

I was watching the 1st Season, 1st Episode of the U.S. Television Series Heroes on DVD when I noticed a clock with Kanji Characters in a scene with Masi Oka (playing Hiro Nakamura). This led me to do this cartoon.

With non-english alphabets that do not share characters, I find it relatively easy to stare at each glyph and relate it to a sound or number and remember it. (My foreign language skills have otherwise languished.) The games Mah-Jong and Shogi have helped enormously to give me practice in this kind of character recognition.

There are some web sites that facilitate this practice:

I hope solving the puzzle in Kanji doesn’t slow you down too much.