# 74: Su Doku

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:[A square divided into 2x2 squares, the top-right one has an 1 in it, the bottom-right one has a 0, the two left ones are empty.] | :[A square divided into 2x2 squares, the top-right one has an 1 in it, the bottom-right one has a 0, the two left ones are empty.] | ||

:Binary Su Doku | :Binary Su Doku | ||

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{{comic discussion}} | {{comic discussion}} |

## Revision as of 20:10, 22 April 2014

Su Doku |

Title text: This one is from the Red Belt collection, of 'medium' difficulty |

## Explanation

Su Doku (Japanese for "single number", and now usually written as "sudoku") is a type of number puzzle, in which the player must place digits in a matrix field in the correct order. The most common arrangement is a 9×9 grid subdivided into nine 3×3 grids where no digit is allowed to appear twice in a horizontal or vertical row on that full 9×9 matrix. The number and combination of pre-filled squares determines the difficulty of the puzzle. When the puzzle is solved each row and column will contain the numbers 1 to 9 in a particular order.

Randall presents just a binary sudoku puzzle. A normal sudoku uses 9 digits, usually 1 to 9, and so fits conveniently into our normal "decimal" counting system (ten digits).

The joke is that the binary system has only two digits (0 and 1), and therefore binary sudoku puzzles would be trivially easy and thus pointless. The puzzle in the comic would be completed by filling 0 in the top-left and 1 in the bottom-left empty box. The only other possible grid would have the 0s and 1s swapped. This fulfills the criteria of having no repeated digits in any row or column. Square sudoku puzzles can only be formed with a square number of digits (4, 9, 16 ...), on grids with a cube number of positions (8, 27, 64 ...). Thus this is not a completely natural extension of the sudoku puzzle to two digits, and could be considered a Latin square problem.

The title text appears to reference a series of published sudoku puzzle books called the "Martial Arts Sudoku". The difficulty of each book is denoted by a martial arts belt color, with each color representing a certain skill level. Since a red belt is a rather high level (second only to a black belt), the fictional authors of this sudoku collection apparently consider this incredibly simple puzzle is rather difficult.

## Transcript

- [A square divided into 2x2 squares, the top-right one has an 1 in it, the bottom-right one has a 0, the two left ones are empty.]
- Binary Su Doku

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# Discussion

If that puzzle is 4 (i.e. 2x2) domains of 1x1 cells or 1 domain of 4x4 cells then it's actually an impossible puzzle. Sudoku grids for 'n' symbols (ignoring some very interesting variants) need to be of n² cells in total with n cells in each direction, composed of n 'domains', each of n cells so as to contain *one and only one* of each symbol in use. That's 81 cells in a traditional 1-9 digit 9x9 format, being 3x3 array of 3x3 individual cells in typical ~~Sudokus~~ ~~Sudokii~~ ~~Sudoka~~ puzzles, but can be irregularly domained instead as long as the domains still have nine cells. In a 12-digit that's often 3x4 cells in each domain, arrayed 4x3 (or 4x3 arrayed 3x4) to make a 12x12 full grid but can be 2x6 6x2s (or <=>) or of irregular, but still equally-sized, subdivisions. ("Killer" variations typically augment the row, column and domain parities with a 'fourth dimension' of *unequally*-sized irregular domains (no larger than any other domain, containing a *maximum* of one of each digit, but possibly zero of some) labelled as having a stated sum total within (more than or equal to m*(m-1)/2 for m cells in that given sum-zone, assuming the lowest digit is 1, and less than or equal to (n*(n-1)/2)-((n-m)*(n-m-1)/2), if n digits are being used as unique symbols throughout the whole grid), but that's generally in leiu of *all* pre-existing clue digits, using Kakuro-like calculations to break ground on the puzzle's answer.)

Realistically, therefore, the comic must be 1x2 domains of 2x1 cells. Or the other way round. Although it's not obvious from the line-weighting which it might be. As each subdivision is the same as the row-grouping or column-grouping it could effectively be just a 'simpler' puzzle that abandons or considers redundant domains *other* than the basic rows and columns, given that each possible domain-type would be congruent with one or other of the two implicit groupings. However, it definitely could *not* be an "X" variant of the puzzle type (repetition dissallowed across the major diagonals, as well as across rows and columns), otherwise it reverts to being impossible again...

However, none of what I've just said is particularly entertaining, so please feel free to ignore it and instead try the following Unary Sudoku.... (Hint: its major diagonals are also valid domains to solve!)

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178.98.31.27 15:07, 24 June 2013 (UTC)

## Major update

I think we even can discus PIxPI grids here at discussion page, but the explain should be simple as possible. Please help on that bad remaining language. AND: Since Randall is from the US we have AE (American English) here.--Dgbrt (talk) 21:19, 1 July 2013 (UTC)

I think this description of the alt text is a little inadequate. The reason the puzzle is 'medium difficulty' is because any given puzzle in a binary sudoku is going to be essentially the same... you'll either have a one and a zero, two ones, or two zeroes since those are the only ways to ensure a unique solution. So all puzzles have the same difficulty which is why it is 'medium'.--108.162.238.162 08:28, 28 July 2015 (UTC)

- I don't follow your sentence "you'll either have a one and a zero, two ones, or two zeroes", please can you try and explain more clearly. Essentially though, there are two possible solutions to the puzzle:

0 1 or alternatively 1 0 1 0 0 1

- The only thing which can make the difficultly change is how many cells are pre-filled. If 0 are filled then either both solutions are correct, or it is impossible to know which solution is correct. If 1 cell is filled, then it is easy to complete the rest of the grid. If 2 are filled, then it is even easier to complete, and easier again with 3 filled. --Pudder (talk) 11:01, 28 July 2015 (UTC)