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An international terminology for the Calcudoku-Kenken?
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Posted on: Thu Nov 10, 2011 11:59 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
An international terminology for the Calcudoku-Kenken?
An international terminology for the Calcudoku-Kenken?.
(A proposal for an international terminology by the Cacudoku-Kenken solving strategies and tips).

I propose that, in order to make unnecessary the use of any particular language, so that any techniques or solution strategies proposed for the Calcudoku-Kenken puzzles can be understood by persons in the different countries, we build and agree some kind of mathematical terminology (like a common musical language or an “esperanto” for the Calcudoku), some kind of simple agreement easy to learn and easy to understand.

My initial suggestion or proposal is this:

1. If a process is made of various steps we will name them 1., 2., etc., with the use of the bolding and a dot though, in parenthesis, optionally, some comments, like the colours used, etc., may be included in the different languages, and this would be the only "free" part in the terminology, example: 1.(...).

2. The cages will be named “75x”, “2-“, “27+”, “4:”, “3mod”, “-4+”, “12|”, …, showing first the result of the operation followed by the type of the operation.

3. The position of the cages (if necessary to avoid uncertainties) will be referred to with parentheses inmediately after the name, in this way: “75x” (e1-f1-f2), with the cell positions separated with dashes and ordering the cells first by the column, then by the row, so (a1-a2-b1-b2) but not (a1-b1-a2-b2). With the same target, the reference to "any" cell of those occupied by the cage will considered enough, for instance: "75x" (e1) or "75x" (f2). Also we write "1280x" (ffff) if we want to refer to certain part of a cage, the part occupying the column f, or "1280x" (5555), in the case of row 5, for instance.

4. The “value” of a cage (the addition of all numbers inside the cage, or the multiplication, etc.) will be shown in this way: “75x” (+) = 13, ”17+” (x) = 300, “3mod” (+) = 8, “5|” (+) = 9, “1^” (+) = 13, etc. In case of including the position of the cage that would be “75x” (e1-f1-f2) (+) = 13 or, i.e., “17+” (a1-a2-b1-b2) (x) = 300.

5. When a cell must have a determined value we will use the equal sign, for instance, b1 = 7. If the cell must be different than a determined value we will use, for instance, c3 <> 5 (a little joke, please avoid the confusion you may create if you use “the mother of all formulas”: x < = > y).

6. If a cell may have several possibilities we write: b1 = 3, 5, 7, … If a cell must be different than several values we write: b1 <> 2, 6, 9, … If a group of cells must have a defined group of values we write: h3-h4 = [3, 5] (square brackets) this means that the 3 and the 5 must occupy the cells h3 and h4, the exact location to be defined later. If various independent cells (not a cage) may take several different values (from a pool) we write, i.e.: (a3, a5, a8) = 3, 4, 5, 6, 9. If various cells (independent or that may be part of a cage) must be different than one or more numbers we write, i.e.: (a3, a8, b3, b4) <> 7, 9 this means that the 7 and the 9 are forbidden for the cells a3, a8, b3 or b4.

7. If a cell must be even we write c3 = 2n. If odd, we write c3 = 2n + 1. If a cage must be even we write "75x" (c5-d5-d6) = 2n. If odd, we write, i.e.: "3:" (f2-g2-g3-h3) = 2n + 1 [The (+) after the cage is assumed in this case].

8. The rule of the addition, i.e., in an 7x7 puzzle, would be: (e+++) = 28; (5+++) = 28, where (e+++) represents the addition of all numbers in column e and (5+++) represents the addition of all numbers in row 5.

9. Similarly, for the rule of the multiplication, i.e., in a 6x6, we would write: (dxxx) = 6! = 720 (factorial of 6) for the column d, or (3xxx) = 6! = 720 for the row 3.

10. The maximum (///) or the minimum (\\\) of a cell, a cage, a sum, etc., would be represented in this way: ///[“0-“ (+)] = 14, etc. Or, for a sum of cages: ///[“0-“ (a4-a5-b5) + “2-“ (b2-b3)] = 16. Or, for an individual cell, \\\[g2] = 4.

11. If a cage must contain a already well defined numbers we say: “75x” (e1-f1-f2) = [3, 5, 5] (with the numbers inside the square brackets in ascending order). If a cage may have several possibilities we write: “120x” (a1-a2-b1-b2) = [2, 3, 4, 5], [2, 2, 5, 6], [1, 4, 5, 6], [1, 3, 5, 8], …; for instance, in a 6x6 puzzle: “300x” (a1-a2-b1-b2) = [3, 4, 5, 5], [2, 5, 5, 6]. If a cage must be different than some specific combination we say, i.e.: “13+” (a3-a4-b3) <> [4, 4, 5] or “13+” <> [4, 4, 5], [3, 5, 5] this last case meaning that both combinations are forbidden.

12. If some of the numbers inside a cage are unknown we write: “5880x” (a2-a3-b3-b4-c4) = [x, y, z, 7, 7]; in this case what we say is that the cage contains two 7’s, being x, y and z, three unknown numbers (in this moment, obviously). We will use for the variables the final letters of the alphabet (t, u, v, w, x, y, z).

13. If a cage can not contain a specific number, i.e, the 3, we write: “14+” (c4-c5-d4) <<>> 3; “14+” (c4-c5-d4) <<>> 3, 5 means that neither the 3 or the 5 can go inside that cage. If a number, i.e., the 7, is already present in a determined line we may use: (eeee) [] 7! or (5555) [] 5!, this meaning that the column e already contains a 7 (or that a 5 is already present in the row 5). Also, if what we want to say is that a certain number is required in a certain line, i.e., the 8 in column f, we would write: 8 >>> (ffff)! or 7 >>> (3333)!.

14. If an hypothesis or a conclusion implies another hypothesis or another conclusion we write: a3 = 4 ---> “3-“ (c3-d3) = [2, 5], [3, 6] or, in case of two or more simultaneous premises: (a3 = 4; b3 = 2) ---> “3-“ (c3-d3) = [3, 6]. A series of consequences would show several consecutive ---> among the statements. If an hypothesis drives to an impossibility we would write: (a3 = 4; b3 = 2) ---> “3-“ (c3-d3) = [3, 6] = [000] (this meaning that the pair [3, 6], i.e. in a 6x6 puzzle, is not allowed in those cells because of other reasons then arriving to the conclusion that the premises are wrong). For “because of” we will use *…* enclosing the explanation between asterisks (it is recommended to minimize the use of “because of”).

15. The first line of the text will always be, i.e.: C = 8 (unnumbered, C stands for "Calcudoku", 8 is the size of the puzzle). After this first line we will write the steps (in ascending order, without lack of numbers). To refer to certain part of a text we will use intermediate lines of ... ... ... (three groups of three dots) or when suppressing part of a text wich is not now significative. The statements will be separated by semicolons. Finally, to indicate the end of the process we will repeat the initial statement C = 8.

An example, using this terminology to answer the jomapil’s question, for the puzzle Nov 07, 2011 (Puzzle id: 380447):

C = 9

1. “42x” (a8-b8) = [6, 7]; a7 = 7 ---> a8 = 6; b8 = 7

2. “9x” (a2-a3) = [1, 9]; “9:” (h9-i9) = [1, 9]; “18x” (f2-f3) = [2, 9]; e3-e4 = [4, 5] ---> e1-e2 = [3, 8] ---> e7-e8 = [2, 9]

3. “6x” (b2-b3) = [1, 6], [2, 3] ---> “6x” (+) = 2n + 1 ---> b9 = 2n

4. b9 <> 2, 4 ---> b9 = 6, 8; b9 = 6 ---> “6x” = [2, 3] ---> “0-“ (a6-b6-b7) (+) = 14 *(a+++) + (b+++) = 90* = [000] (Note * below) ---> b9 = 8 ---> c9 = 3 ---> e9 = 6 ---> e5-e6 = [1, 7] ---> f6 = 4

5. “6x” (+) + “0-“ (a6-b6-b7) (+) = 17; “6x” = [2, 3] ---> “0-“ (+) = 12 = [000] (Note ** below) ---> “6x” = [1, 6] ---> “0-“ (+) = 10 ---> “0-“ = [2, 3, 5]

6. “840x” (g1-g2-h1-h2) = [u, v, w, 7]; “588x” (g3-h3-h4-i4) = [x, y, 7, 7]; (“840x”; “588x”) ---> “8+” (i5-i6) <> [1, 7]; “8+” = [3, 5] ---> i6 = 3 *f5 = 3* ---> b7 = 3 ---> a6-b6 = [2, 5] ---> “6+” (c5-c6) <> [1, 5], [2, 4] = [000] ---> “8+” = [2, 6] ---> “18+” (i1-i2-i3) <<>> 7 ---> i4 = 7 ---> i8 + i9 = 4 *(i+++) - 18 - 7 - 8 - 8 = 4* ---> i8 = 3 ---> i9 = 1 ---> h9 = 9 ---> “18+” = [4, 5, 9]; i2-i3 <<>> 9 ---> i1 = 9 ---> i2-i3 = [4, 5]

7. “588x” = [2, 6, 7, 7], [3, 4, 7, 7]; (d3 = 3; e3-i3 = [4, 5]) ---> “588x” <> [3, 4, 7, 7] ---> “588x” = [2, 6, 7, 7]

… … …

C = 9

The full solution would not extend for more than 18 or 20 steps and no more than half a page for a 9x9 puzzle.

I think then that the use of a terminology like this could have some advantages:

- An “international” agreement, a quick way of “speaking” with numbers and signs (implicitly we are already using part of this “language” in our Forum, intuitively).

- The solutions could be compiled by the programmers and converted to a representation with graphics, etc., with the significative numbers flashing, bolded, etc.

- Inversely, a computer´s presentation (which includes a representation with graphics) could automatically be translated generating the appropriate terminology (the “object” file) to be understood by any puzzlers regardless of the country/language.

- No voice is really required (but perhaps it may be introduced in the optional parenthesis of the steps).

Note *: I have exceptionally added this note to remind that (see previous posts) if a cage “n-“ has an “addition” value of V, the higher number inside the cage is (n + V) / 2 so, in this case, if the cage “0-“ had a value of 14, the higher number inside (that must be necessarily present) would be (0 + 14) / 2 = 7 and this is impossible due to the 7’s occupying the cells a7 and b8.

Note **: Neither of [1, 5, 6] or [2, 4, 6] or [3, 3, 6] are possible for “0-“ (a6-b6-b7)

Last edited Nov 11, 2011 to add graphics and correct some typo errors.
Reedited Nov 12, 2011 to correct some typo errors and make more clear some statements.
Reedited several times Nov 14, 2011 to improve the terminology.
Reedited several times Nov 15, 2011 to make more clear some statements.
Reedited several times Nov 22, 2011 to correct some typo errors and improve the terminology.
Reedited Nov 27, 2011 to improve the terminology.

Last edited by clm on Sun Nov 27, 2011 1:09 pm, edited 18 times in total.

Posted on: Fri Nov 11, 2011 1:11 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: An international terminology for the Calcudoku-Kenken?
It's very interesting and useful.
Why in 15) you present >>> and no the more frequent -->?
In the second note if we can calculate (n+V)/2 we obtain the upper limit for the value of the cells, Why did you say " this is impossible ". Of course on account the 7's already known the cells can't be 7. But in this context 7 will be the upper value and not a possible value. Do you want to tell other thing?

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Posted on: Fri Nov 11, 2011 5:22 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: An international terminology for the Calcudoku-Kenken?
jomapil wrote:
It's very interesting and useful.
Why in 15) you present >>> and no the more frequent -->?
In the second note if we can calculate (n+V)/2 we obtain the upper limit for the value of the cells, Why did you say " this is impossible ". Of course on account the 7's already known the cells can't be 7. But in this context 7 will be the upper value and not a possible value. Do you want to tell other thing?

It is something to start... the terminology is made initally by those 15 paragraphs... but subjected to additions, modifications... . With respect to "this implies that..." yes, I absolutely agree with you, I prefer the horizontal arrow as in maths. I prepared the text with the "Word" processor, I do not have the horizontal arrow directly in my keyboard, then when typing two consecutive dashes and the character > the text processor joined all giving an arrow, so I thought it was Ok, but at the moment of submitting the post to the Forum, here it appeared instead a small square in all places (I do not know why, ASCII code, the language of my keyboard, etc.). I modified all directly in real-time in the Forum's window, but I certainly prefer the -->. My "Word" do this well (if I leave an space between the second dash and the >) so initially I will reedit the post (this afternoon) and change all again (I have to reedit the post anyway to add the 9x9 graphics referred to, only the original puzzle and the solution).

You have probably observed that e9 = 6 can be inmediately obtained, and consequently "11+" (b9-c9) = [3, 8] placing the 3 in c9 (b9= 8) according to parity rules; however I have preferred to solve the "indetermination" of cage "11+" (b9-c9) first, via the analysis shown, to practice a little bit with the concepts though mainly to practice with this new terminology (I have not seen yet the sneaklyfox's video on this puzzle so I do not know if I am being redundant or following a different way).

When I said " ... and this is impossible ... " I was referring to the 7 as the higher number (the other two numbers in the cage would have been lower and subtracted from the 7) inside the cage "0-" (a6-b6-b7) and this is obvious in this particular case because there are already two 7's in columns a and b, in the cells a7 and b8, so this cage could never contain a 7 or have an "addition value" of 14. If the explanation is confuse or not well expressed (my English) pse tell me to try modify the text.

P.D.: I am specially interested in the 15 paragraphs, the body of the "terminology", is the English correct? Are the ideas and concepts well explained and understood?.

Posted on: Fri Nov 11, 2011 8:11 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: An international terminology for the Calcudoku-Kenken?
The text is very well explained. Concerning your English, for me is perfect ( I can't tell the same from my own and every time I write something here at the Forum I do it with some shame on account of the blunders ). ( Quiçá en Español yo escribiria mejor! ).
Concerning to any changes, for me I don't think any alterations, when the time goes by maybe appears any sugestion.
In short, in my humble opinion it's everything OK!

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Posted on: Tue Nov 22, 2011 9:48 am

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: An international terminology for the Calcudoku-Kenken?
With the purpose to lighten some aspects I suggest the following:

1) The names of cells ( b7 ) and cages ( 27+ ) have different configurations. So I would not use the "" in the designation of the cages.

“840x” (g1-g2-h1-h2) = [u, v, w, 7] --> 840x (g1-g2-h1-h2) = [u, v, w, 7]

2) It would not be necessary the inclusion of all the cells of a cage but only the cell where is the value of the cage.

840x (g1-g2-h1-h2) = [u, v, w, 7] --> 840x (g1) = [u, v, w, 7]

3) If there is only one cage in the puzzle with the value of that cage it's not necessary to indicate the name of the first cell

840x (g1) = [u, v, w, 7] --> 840x = [u, v, w, 7]

This 3rd suggestion can be optional.

Maybe there is a reason for the original ideas. If so ...

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Posted on: Tue Nov 22, 2011 1:47 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: An international terminology for the Calcudoku-Kenken?
jomapil wrote:
With the purpose to lighten some aspects I suggest the following:

1) The names of cells ( b7 ) and cages ( 27+ ) have different configurations. So I would not use the "" in the designation of the cages.

“840x” (g1-g2-h1-h2) = [u, v, w, 7] --> 840x (g1-g2-h1-h2) = [u, v, w, 7]

I think it is necessary to maintain the quotes for the cages because, i.e., 5+ may be interpreted as an arithmetic operation along the text, etc... (see, for instance, its importance for the compiler of the Forum, in our posts, see the effect when we say: quote="clm")

jomapil wrote:
2) It would not be necessary the inclusion of all the cells of a cage but only the cell where is the value of the cage.

840x (g1-g2-h1-h2) = [u, v, w, 7] --> 840x (g1) = [u, v, w, 7]

This is very interesting to simplify the terminology, I will quickly introduce it, and even for "any" of the cells of the cage, like "840x" (h1) though no objections if the full position is given.

jomapil wrote:
3) If there is only one cage in the puzzle with the value of that cage it's not necessary to indicate the name of the first cell

840x (g1) = [u, v, w, 7] --> 840x = [u, v, w, 7]

This 3rd suggestion can be optional.

Maybe there is a reason for the original ideas. If so ...

This was already included in the terminology "3. The position of the cages (if necessary to avoid uncertainties) will be referred ..." so it's already optional if there are not uncertainties (in the example given in the original post, in step 7, I intentionally refer to the cage "588x" without the position because it is unique), the idea was defining the position when there are two or more cages "840x". Thank you very much.

Posted on: Sat Nov 26, 2011 11:50 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: An international terminology for the Calcudoku-Kenken?
Hi, Clm.

I finished to solve a puzzle 9x9 to post at the Forum and it appears some situations not thought:
When a cage occupies 2 columns when I wanted refer to only the part of the cage in a determined column I said "12+"(e) <<>>5. The column e of the cage "12+" doesn't contain the number 5.
I think a letter or a number alone ( without more sinals or symbols can represent a column or a row without ambiguity.
I felt another necessity. At the following equation
h2 = g9 - "4-"(i2)(+) +5
"4-"(i2)(+) ( the addition of all the cells of the cage "4-" beginning from the cell i2 ) can be simpler, for instance, "4-,+"(i2) or another way.

What do you think?

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Posted on: Sun Nov 27, 2011 1:05 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: An international terminology for the Calcudoku-Kenken?
jomapil wrote:
Hi, Clm.

I finished to solve a puzzle 9x9 to post at the Forum and it appears some situations not thought:
When a cage occupies 2 columns when I wanted refer to only the part of the cage in a determined column I said "12+"(e) <<>>5. The column e of the cage "12+" doesn't contain the number 5.
I think a letter or a number alone ( without more sinals or symbols can represent a column or a row without ambiguity.

This is a good idea, the last time the paragraph 6. was modified something was missing, I have included now the "doesn't contain" condition for "part of a cage" and even for a group of independent cells (that may be or may be not part of a cage). And I have also extended the paragraph 3. to include the reference to part of a cage in a certain row or column, also avoiding the uncertainties and making consistent the terminology with the use of the redundant letter or number, i.e., "1280x" (5555) because a single 5 like "1280x" (5) would create confusion (not in the case of the letters, but the redundancy is for consistency).

jomapil wrote:
I felt another necessity. At the following equation
h2 = g9 - "4-"(i2)(+) +5
"4-"(i2)(+) ( the addition of all the cells of the cage "4-" beginning from the cell i2 ) can be simpler, for instance, "4-,+"(i2) or another way.

What do you think?

I think that perhaps it is better to show equations like these in this way: h2 + "4-" (i2) = g9 + 5, so reducing the number of minus signs; but I am not inclined to introduce two different signs inside the quotes for a cage because we would break the "definition" of the cage (paragraph 2.) and create some confusion, for the moment the idea with the terminology is that it be clear and "easy" to understand (though enough rich in the "vocabulary") with the time and the use, and if it has acceptance, we may go to a more concise expressions.

(By the way, I will make the translation for the Spanish Forum every two months or so to resume the changes, so in this moment is not actualized)

Posted on: Sun Nov 27, 2011 3:03 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: An international terminology for the Calcudoku-Kenken?
clm wrote:
I think that perhaps it is better to show equations like these in this way: h2 + "4-" (i2) = g9 + 5,

You are right. But in this equation you missed a signal +. Is this intentionally?
Because in an equation like that, the term "4-"(i2) is assumed to be an addition?

i.e. "4-"(i2)(+) is equal to "4-"(i2) in an equation?

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Posted on: Sun Nov 27, 2011 3:43 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: An international terminology for the Calcudoku-Kenken?
jomapil wrote:
clm wrote:
I think that perhaps it is better to show equations like these in this way: h2 + "4-" (i2) = g9 + 5,

You are right. But in this equation you missed a signal +. Is this intentionally?
Because in an equation like that, the term "4-"(i2) is assumed to be an addition?

i.e. "4-"(i2)(+) is equal to "4-"(i2) in an equation?

Yes, we may include it optionally, but not necessarily, it is easily assumed in a linear equation with only sums, as, in this other example: h2 x "4-" (i2) x ... = 2 x 9! = 725760 where we are assuming that we are multiplying h2 x "4-" (i2) (x) x ... by the rest of the elements of columns h and i, so we are referring to the "product value" of cage "4-", in this way we simplify a little bit the expressions without confusion.

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