OK I have had some requests for puzzles....
Try this:
********4
4*21**356
***54**98
--------------
****86431
6*1***2*9
89423****
--------------
12**59***
953**46*2
7********
Let me know how you do......
Friday, October 14, 2005
Tuesday, October 11, 2005
Math Games:Sudoku Variations
Math Games:Sudoku Variations: "Who made this puzzle? In addition to being the crossword editor of the New York Times, Will Shortz is a puzzle historian, so he did detective work to find the answer. He knew that 'Number Place' puzzles had appeared in Dell Magazines, and went through his collection to find the first. Dell listed no author, but the name Howard Garns always appeared in the contributor's list of any issue containing a 'Number Place' puzzle. Also, Garns' name did not appear in any issue lacking a Number Place, which clinched the identification. Further research revealed that Howard Garns to be a retired architect who created the puzzle at age 74. Howard Garns died in Indianapolis in 1989, and never got a chance to see his creation as a worldwide phenomenon. (Shortz, pers. comm. 2005)
Howard Garns made many Number Place puzzles for Dell, quickly simplifying the rules to those used today -- Fill in the grid so that every row, column, and 3x3 box contains the digits 1 through 9. In April 1984, Japan's puzzle group Nikoli discovered Dell�s Number Place presented it for a Japanese audience in the pages of puzzle paper Monthly Nikolist. Originally named Suuji Wa Dokushin Ni Kagiru, ('the numbers must be single') the puzzle became very popular. Kaji Maki, the president of Nikoli, abbreviated it to Sudoku - (Su = number, Doku = single), and trademarked the name. As the popular grew, competing companies stayed with the non-trademarked name Number Place, or 'nanpure'. Even today, many Japanese puzzle magazines spell out 'Number Place' in English. In the United States and elsewhere, it's called Sudoku ('single number' in Japanese). Thus, japanese-speakers use the English, and english-speakers use the Japanese. Here are two particularly nice Sudoku puzzles under the normal rules. "
Howard Garns made many Number Place puzzles for Dell, quickly simplifying the rules to those used today -- Fill in the grid so that every row, column, and 3x3 box contains the digits 1 through 9. In April 1984, Japan's puzzle group Nikoli discovered Dell�s Number Place presented it for a Japanese audience in the pages of puzzle paper Monthly Nikolist. Originally named Suuji Wa Dokushin Ni Kagiru, ('the numbers must be single') the puzzle became very popular. Kaji Maki, the president of Nikoli, abbreviated it to Sudoku - (Su = number, Doku = single), and trademarked the name. As the popular grew, competing companies stayed with the non-trademarked name Number Place, or 'nanpure'. Even today, many Japanese puzzle magazines spell out 'Number Place' in English. In the United States and elsewhere, it's called Sudoku ('single number' in Japanese). Thus, japanese-speakers use the English, and english-speakers use the Japanese. Here are two particularly nice Sudoku puzzles under the normal rules. "
Saturday, October 08, 2005
Solving Sudoku
Solving Sudoku: "Hidden Singles:
Very frequently, there is only one candidate for a given row, column or 3x3 box, but it is hidden among other candidates.
In the example on the right, the candidate 6 is only found in the middle right cell of the 3x3 box. Since every 3x3 box must have a 6, this cell must be that 6."
Very frequently, there is only one candidate for a given row, column or 3x3 box, but it is hidden among other candidates.
In the example on the right, the candidate 6 is only found in the middle right cell of the 3x3 box. Since every 3x3 box must have a 6, this cell must be that 6."
Friday, October 07, 2005
Sudoku Discussions: A little tip to help solve the puzzles
Sudoku Discussions: A little tip to help solve the puzzles: "Now, at the more tactical level:
1 - if, let's say 3-9, 3-9 appear in the same row (or column), then neither 3 or 9 can occur anywhere else in that row (column). If a pair like that occurs in a 3x3 box, then those values cannot appear anywhere else in that 3x3 box.
If a triple occurs (say 3-6-9) three times in the same column (row, 3x3 box), then those three values cannot occur anywhere else in that column (row, 3x3 box).
NOTE that these numbers must occur without any additional values (e.g, 2-4, and 2-4-7 does not tell you anything - you can't assume anything special about 2 and 4).
I usually mark the values that _can_ occur in an empty entry. Then I look at a row (column, 3x3 box) and see if a value occurs in only one entry (then it has to go there), or if I'm looking at a row or column, if it occurs more than once, but only in a single 3x3 box.
As noted by john mcintosh, three entries that involve three possible numbers (e.g., 1-2, 1-3, 2-3) occurring in a row, column or 3x3 box, also allow you to eliminate those values from occurring anywhere else in that row, column, or 3x3 box.
I hope this hasn't been too confusing. It would be nice if we had a standard notation and terminology as does chess.
I have found that using the techniques above, it has never been necessary to resort to bifurcation. In fact, I've not found a case where bifurcation was helpful (the chain of logic was too long and turned the approach into a form of restricted guessing). It could be that I've just done the wrong puzzles and that eventually I'll hit one where bifurcation is necessary and works, however, I think that would indicate an ill-composed puzzle. "
Sudoku is addictive and helps take your mind off the day
1 - if, let's say 3-9, 3-9 appear in the same row (or column), then neither 3 or 9 can occur anywhere else in that row (column). If a pair like that occurs in a 3x3 box, then those values cannot appear anywhere else in that 3x3 box.
If a triple occurs (say 3-6-9) three times in the same column (row, 3x3 box), then those three values cannot occur anywhere else in that column (row, 3x3 box).
NOTE that these numbers must occur without any additional values (e.g, 2-4, and 2-4-7 does not tell you anything - you can't assume anything special about 2 and 4).
I usually mark the values that _can_ occur in an empty entry. Then I look at a row (column, 3x3 box) and see if a value occurs in only one entry (then it has to go there), or if I'm looking at a row or column, if it occurs more than once, but only in a single 3x3 box.
As noted by john mcintosh, three entries that involve three possible numbers (e.g., 1-2, 1-3, 2-3) occurring in a row, column or 3x3 box, also allow you to eliminate those values from occurring anywhere else in that row, column, or 3x3 box.
I hope this hasn't been too confusing. It would be nice if we had a standard notation and terminology as does chess.
I have found that using the techniques above, it has never been necessary to resort to bifurcation. In fact, I've not found a case where bifurcation was helpful (the chain of logic was too long and turned the approach into a form of restricted guessing). It could be that I've just done the wrong puzzles and that eventually I'll hit one where bifurcation is necessary and works, however, I think that would indicate an ill-composed puzzle. "
Sudoku is addictive and helps take your mind off the day
Sudoku Discussions: A little tip to help solve the puzzles
Sudoku Discussions: A little tip to help solve the puzzles: "First of all, I think of the game as being made up not only of nine rows and columns, but also three 'broad' rows and columns, 3x3 boxes, and little boxes I call 'entries'.
My first step is to examine broad columns from left to right, then broad rows from top to bottom.
Let's say we're looking at a broad column. The 'examination' involves looking at pairs of values that occur in the broad column. If the same number appears twice, that eliminates two broad rows in that broad column. It also restricts us to look at the narrow column that the other two values are _not_ in. If that column has only one empty space, the value goes there. If it has more than one, but the number occurs in enough of the rows crossing the column, the number can be placed uniquely. If neither of these is true, you only know the value has to go in that column.
Each time I can fill in a value, I look at the effect that has on the broad row in which it occurred. I follow this logic until I can't fill that value in anywhere else. Now, following this general scheme, you make (in a sense) one pass through the puzzle's broad columns and rows and you've filled in all the 'easy' values.
Now I look at the boxes that are most-filled-in (usually you'll have at least one box with five values filled in). I look at the values that are missing and see if any of them can occur in only one place in the box. I do the same for the most-filled-in rows and the most-filled-in columns. In particular, look for positions where a most-filled-in column crosses a most-filled-in row at a blank entry.
I will continue to add more insights here.
My first step is to examine broad columns from left to right, then broad rows from top to bottom.
Let's say we're looking at a broad column. The 'examination' involves looking at pairs of values that occur in the broad column. If the same number appears twice, that eliminates two broad rows in that broad column. It also restricts us to look at the narrow column that the other two values are _not_ in. If that column has only one empty space, the value goes there. If it has more than one, but the number occurs in enough of the rows crossing the column, the number can be placed uniquely. If neither of these is true, you only know the value has to go in that column.
Each time I can fill in a value, I look at the effect that has on the broad row in which it occurred. I follow this logic until I can't fill that value in anywhere else. Now, following this general scheme, you make (in a sense) one pass through the puzzle's broad columns and rows and you've filled in all the 'easy' values.
Now I look at the boxes that are most-filled-in (usually you'll have at least one box with five values filled in). I look at the values that are missing and see if any of them can occur in only one place in the box. I do the same for the most-filled-in rows and the most-filled-in columns. In particular, look for positions where a most-filled-in column crosses a most-filled-in row at a blank entry.
I will continue to add more insights here.
Sudoku Discussions: A little tip to help solve the puzzles
Sudoku Discussions: A little tip to help solve the puzzles: "So far this method has worked.
1 After obvious initial entries fill in the blank cells with all allowable numbers.
Now look for a single occurence of any one number:
a) in any row
b) in any column
c) in any of the boxes
when you find a single occurrence then that is the number . Now eliminate that number from the box and row and column.
Then look for another singleton and repeat the process when you find one."
1 After obvious initial entries fill in the blank cells with all allowable numbers.
Now look for a single occurence of any one number:
a) in any row
b) in any column
c) in any of the boxes
when you find a single occurrence then that is the number . Now eliminate that number from the box and row and column.
Then look for another singleton and repeat the process when you find one."
Sudoku Online : Sudoku Helper
Sudoku Online : Sudoku Helper: "To really show what goes on when the script checks your board the Take Step button runs through four tests:
Rows and Columns - fills in the blanks with possible numbers by looking at the existing numbers in each row and column. If only one value is possible its written to the board in a large blue colour.
Each Box - does the same as the first test but it looks to eliminate possibles by checking all the existing numbers in each of the nine 3 by 3 boxes.
Pairs Test. We know we can eliminate numbers if two squares have two identical pairs of numbers. For example, if a row has 3-7 and 3-7 then all other 3s and 7s in that row can be eliminated. Same goes for the box and column.
Box/Line reduction: This is part of the Box tests but I've seperated it so it can be seen. We check the box against the rows and columns that intersect it for each number. See here for more.
The actual tests are slightly more in depth that I have space to explain here. Doubtless there are other strategies that this helper can employ and these will be added in the future. The purpose however is to help you check that your own paper and pencil strategy hasn't introduced any mistakes. "
Sudoku is just too much fun. The real test is to evaluate all the rows, columns, and boxes to eliminate as many candidates as possible.
Rows and Columns - fills in the blanks with possible numbers by looking at the existing numbers in each row and column. If only one value is possible its written to the board in a large blue colour.
Each Box - does the same as the first test but it looks to eliminate possibles by checking all the existing numbers in each of the nine 3 by 3 boxes.
Pairs Test. We know we can eliminate numbers if two squares have two identical pairs of numbers. For example, if a row has 3-7 and 3-7 then all other 3s and 7s in that row can be eliminated. Same goes for the box and column.
Box/Line reduction: This is part of the Box tests but I've seperated it so it can be seen. We check the box against the rows and columns that intersect it for each number. See here for more.
The actual tests are slightly more in depth that I have space to explain here. Doubtless there are other strategies that this helper can employ and these will be added in the future. The purpose however is to help you check that your own paper and pencil strategy hasn't introduced any mistakes. "
Sudoku is just too much fun. The real test is to evaluate all the rows, columns, and boxes to eliminate as many candidates as possible.
The Velvet Blog: Do do sudoku that you do so well
The Velvet Blog: Do do sudoku that you do so well: "Do do sudoku that you do so well
They're all the rage, worldwide. Millions upon millions of people are obsessed with them. And I just don't understand--at all.
They're sudoku, and blame the Japanese for this global craze.
The point of these puzzles is that the numbers 1 through 9 should appear once and only once in any row or column. And I've read a number of explanations of how to do this ... but I just can't. My mind simply goes numb after looking at that grid for more than 10 seconds. For that matter, my mind goes numb after reading the instructions.
I like puzzles, really I do. But I hate these damned things."
They're all the rage, worldwide. Millions upon millions of people are obsessed with them. And I just don't understand--at all.
They're sudoku, and blame the Japanese for this global craze.
The point of these puzzles is that the numbers 1 through 9 should appear once and only once in any row or column. And I've read a number of explanations of how to do this ... but I just can't. My mind simply goes numb after looking at that grid for more than 10 seconds. For that matter, my mind goes numb after reading the instructions.
I like puzzles, really I do. But I hate these damned things."
math_d0rk: SUDOKU!!!!!!!!!!!!!!!
math_d0rk: SUDOKU!!!!!!!!!!!!!!!: "SUDOKU!!!!!!!!!!!!!!!
Sudoku (Japanese: ??, sudoku), sometimes spelled Su Doku, is a placement puzzle, also known as Number Place in the United States. The aim of the puzzle is to enter a numeral from 1 through 9 in each cell of a grid, most frequently a 9�9 grid made up of 3�3 subgrids (called 'regions'), starting with various numerals given in some cells (the 'givens'). Each row, column and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Its grid layout is reminiscent of other newspaper puzzles like crosswords and chess problems. Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005.
There just isn' enough time in the day to play Sudoku. The real object is a process of elimination. Get rid of as mant numbers as you can and then sift through what you have left.
Sudoku (Japanese: ??, sudoku), sometimes spelled Su Doku, is a placement puzzle, also known as Number Place in the United States. The aim of the puzzle is to enter a numeral from 1 through 9 in each cell of a grid, most frequently a 9�9 grid made up of 3�3 subgrids (called 'regions'), starting with various numerals given in some cells (the 'givens'). Each row, column and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Its grid layout is reminiscent of other newspaper puzzles like crosswords and chess problems. Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005.
There just isn' enough time in the day to play Sudoku. The real object is a process of elimination. Get rid of as mant numbers as you can and then sift through what you have left.
Rantlust � Blog Archive � Sudoku
Sudoku: "I have never been a fan of crossword puzzles though I have used them as a means to escape boredom during long train journeys across Siberia or Australia. Now, I have found a perfect replacement and I use it even during the daily commute: Sudoku. Even though Sudoku has been around for a while and extremely popular in Japan, it gained worldwide appeal only this year and suddenly, you cannot go to a bookstore without seeing tons of books on it.
The puzzle consists of a 9x9 grid with nine 3x3 subgrids - three per row and column. The puzzle comes with a few of the 81 cells filled in with some numbers. The goal is to fill out the remaining provided each number appears only once per row, column or subgrid. This is based on logic reasoning alone and do not require any mathematical prowess. The numbers could well be replaced with symbols or alphabets. The puzzles are of varying difficulties. "
For an online version, click on the image. Be warned - it's very addictive. I picked up my Sudoku Masters Course and I have not been able to stop playing this stupid game.
The puzzle consists of a 9x9 grid with nine 3x3 subgrids - three per row and column. The puzzle comes with a few of the 81 cells filled in with some numbers. The goal is to fill out the remaining provided each number appears only once per row, column or subgrid. This is based on logic reasoning alone and do not require any mathematical prowess. The numbers could well be replaced with symbols or alphabets. The puzzles are of varying difficulties. "
For an online version, click on the image. Be warned - it's very addictive. I picked up my Sudoku Masters Course and I have not been able to stop playing this stupid game.
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