How To Find The Formula Of This Permutations? (1 Viewer)

[hopestar]

Hi to all of you guys here…
May this thread fits on this section. A friend of mine gave me this enigma. It is written in Excel format. Since here I can’t attach .xls file, I don't know how to put the file, name Enigma.xls.
There are infinite amount of tables, with ten rows (row 0,1,2,….9) each. Inside of each tables, there are numbers from 1 to 92, 93 to 184, 185 to 276, and 277 to 284, which lie on their certain rows. Here I gave the example tables that have been filled in for 40 tables. By finding the patterns/ formulas, my friend asked me to extend the tables to fill in the blank tables 41,42,43,etc as given beneath of Table 40. Just like SUDOKU, in each tables there will be no same numbers vertically, horizontally and diagonally. If these tables are using permutations from an ideal table that you can see beneath Table 40 (supposed the ideal table was right), then how to find the formulas of its permutations?
Can somebody help me about this?
Thx.
Hope my English is good enough for explaining this.

 

[rowdyroddy]

lol fail english...
set it out better

 

[hopestar]

Hi rowdyroddy,
would you mind helping me to re-write this thread again, so everybody can understand it clearly?
Thx.

 

[khorne]

Screenshot the xls.

 

[rowdyroddy]

Hi guys
A friend of mine gave me this enigma to do

written in excel but i cant attach .xls file
enigma:
There is an infinite amount of tables, with ten rows (row 0,1,2,......9) in each.
Inside each table is numbers 1 to 92,93 and 184, 185 to 276 and 277 to 284 which lie on their certain rows.

Here I gave the example tables that have been filled in for 40 tables. By finding the patterns/ formulas, my friend asked me to extend the tables to fill in the blank tables 41,42,43,etc as given beneath of Table 40.

Like SUDOKU no 1 number can be the same vertically, horizontally and diagonally.

If these tables are using permutations from an ideal table that you can see beneath Table 40 (supposed the ideal table was right), then how do you find the formula for its permutation?

thanks

 

[hopestar]

Thx rowdyroddy,
Then how I suppose to say about this?

May this explanation make the problems become more clearly. Since numbers 93-184 and 185-276 look similar to numbers 1-92, then I subtracted 92 from numbers 93-184 (as tables on hidden columns AE-AX) and subtracted 184 from numbers 185-276 (as tables on hidden columns BZ-CT).
Although this thread has been posted everywhere, but nobody can answer it yet. It’s very tough indeed. Numbers at the right side of each tables are total amount of numbers of each rows, it isn’t total SUM of numbers of each rows. Tables 1 and 4 both have the number 5 in cell {2,2}. Many others same thing happen as if there’s no connection from Table 1 to Table 2 (or other tables). So far I can recognize only patterns of the red & blue numbers as I described on Note: beneath Table 43:

The red numbers (1,5,9,13,17,41,45,49,53,57) never touch row 9, as the blue numbers (21,25,29,33,37,61,65,69,73,77) never touch row 0 (but it occurs on Table 9).
Number 1 will never be in the below row of number 5, number 5 will never be in the below row of number 9, number 9 will never be in the below row of number 13, number 13 will never be in the below row of number 17.
Number 41 will never be in the below row of number 45, number 45 will never be in the below row of number 49, number 49 will never be in the below row of number 53, number 53 will never be in the below row of number 57.
Number 21 will never be in the below row of number 25, number 25 will never be in the below row of number 29, number 29 will never be in the below row of number 33, number 33 will never be in the below row of number 37.
Number 61 will never be in the below row of number 65, number 65 will never be in the below row of number 69, number 69 will never be in the below row of number 73, number 73 will never be in the below row of number 77.

But these do not happen to black & green numbers.
And there’s like an ANOMALY on Table 9. Number 17 touches row 9, which on other tables number 17 is maximum touch row 8. Numbers 113,117,153 touch row 0, where they usually supposed not to be there.

Then I temporary concluded, perhaps an ideal table could be like this?

0 1 41 81 2 42 82 3 43 83 4 44 84
1 5 45 85 6 46 86 7 47 87 8 48 88
2 9 49 89 10 50 90 11 51 91 12 52 92
3 13 53 14 54 15 55 16 56
4 17 57 18 58 19 59 20 60
5 21 61 22 62 23 63 24 64
6 25 65 26 66 27 67 28 68
7 29 69 30 70 31 71 32 72
8 33 73 34 74 35 75 36 76
9 37 77 38 78 39 79 40 80

So many numbers in one row have difference = 4 (as numbers in circles/ovals). Besides, any numbers can be in the same one row with any other numbers, but if you take a look at the tables more carefully, (looks like) only numbers 37 (129/221) and 41 (133/225) will never be in the same one row.

Now how to scramble numbers to result like that..??


<meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 9"><meta name="Originator" content="Microsoft Word 9"><link rel="File-List" href="file:///C:/DOCUME%7E1/komp1/LOCALS%7E1/Temp/msoclip1/07/clip_filelist.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <woNotOptimizeForBrowser/> </w:WordDocument> </xml><![endif]--><style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} h1 {margin-right:0in; mso-margin-top-alt:auto; mso-margin-bottom-alt:auto; margin-left:0in; mso-pagination:widow-orphan; mso-outline-level:1; font-size:24.0pt; font-family:"Times New Roman";} a:link, span.MsoHyperlink {color:blue; text-decoration:underline; text-underline:single;} a:visited, span.MsoHyperlinkFollowed {colorurple; text-decoration:underline; text-underline:single;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style> For khorne,
You can download the file at Mediafire.com (a file hosting service) name Enigma.xls:
[FONT=&quot]Free File Hosting Made Simple - MediaFire[/FONT]
Thx.

 

[rowdyroddy]

um yep... totally agree lol
i do general maths btw so a big wtf from me

 

[hopestar]

um yep... totally agree lol
i do general maths btw so a big wtf from me

That's all you can do?

 

[rowdyroddy]

yeh? i do general maths, in year 12
obviously i have no idea about the question you posted lol

 

[hopestar]

Dear 3unitz,
Someone in other forum gave me this answer :

so basically it looks like you want a random number generator with some restrictions.
firstly, for each table you only want to use each number 1- 92 once.
secondly, no row should have more than 20 numbers.
thirdly, you have four groups of numbers n mod 4. the four groups are further divided into three groups each, n <=40, 40<n<=80, rest. no number in a group that's less than another number in that same group should appear in a row below the larger number.
that is for example, group1 will be 1,5,9, etc up to 40. and 1 won't be below 5 or 9 nor will 5 be below 9.

here's my suggested algorithm.
first start with the optimal group.
1
5
9
13
17
21
25
29
33
37
then going down the list, randomly place a number on any row above it up to the previous number.

Code:
row = 0
for i in range(1,10):
row = random.randint(row,i)
then you can randomly shift rows down if there is any empty rows.

Code:
row = 10
for i in range(0,10):
row = row-1
if row is empty:
white = white +1
else:
newrow = random.randint(row,row+white)
execute this code for each of the 12 groups, and you should get what you are looking for.

What do you think? I didn't try it yet, and I'll tell you later where this came from.
Thx.

 

[hopestar]

i also dont think they are filled in randomly into the rows using a random number generator. for example, theres an obvious restriction on the number 1 to be in either row 0 or 1. for 70% of the 1's to land in the same row (out of 10 rows and 40 trys) if they are distributed randomly is astronomical. also, 11/12 times the 1 has been on row 1, the number 41 was placed above it. once again this seems to violate odds of a random distribution.

im more inclined for this reason to say theres some sort of pattern behind the distribution of the numbers into rows.

Total amount of numbers of all tables = 284 numbers*40 tables = 11,360 numbers.
Average = 11,360/10 rows = 1,136 numbers.
Here below the list of total numbers of each rows from all of tables:

Row 0 =1,124
Row 1 =1,143
Row 2 =1,041
Row 3 =1,170
Row 4 =1,192
Row 5 =1,165
Row 6 =1,114
Row 7 =1,153
Row 8 =1,120
Row 9 =1,138
Total = 11,360

Total numbers of each rows almost reach the average. It made me believe this is just cryptography random.
Honestly, I'm so poor in computer & programming, but I've tried the codes in VB.Net 2008, it didn't work.
Thx.

 

[hopestar]

41 49 61 3 4 6 8 12
5
57 21
1
53 77
11 14
25 33 69 73 2
9 13 37 10 15
17 29 7
45 16


I've seen the result and there are several mistakes:


Number 5 is above 1,9,13,17.
It should be number 1 is never beneath 5, 5 is never beneath 9, 9 is never beneath 13, 13 is never beneath 17.


Number 33 & 37 are above 29.
It should be number 21 is never beneath 25, 25 is never beneath 29, 29 is never beneath 33, 33 is never beneath 37.


Number 49 is above 45 & 57, and number 57 is above 45 & 53.
It should be number 41 is never beneath 45, 45 is never beneath 49, 49 is never beneath 53, 53 is never beneath 57.


Number 77 is above 69 & 73.
It should be number 61 is never beneath 65, 65 is never beneath 69, 69 is never beneath 73, 73 is never beneath 77.
Where's number 65 anyway?


Ok, I have to learn Java

Thx.

 

[hopestar]

i dont think this ideal table is correct. one thing about all 40 tables is that they are "filled in" from the left; gaps only exist to the right and no where in-between 2 numbers (for example the gap between 53 and 14 in your ideal table).

<style type="text/css"> <!-- @page { margin: 0.79in } P { margin-bottom: 0.08in } --> </style> 0 1 41 81 2 42 82 3 43 83 4 44 84
1 5 45 85 6 46 86 7 47 87 8 48 88
2 9 49 89 10 50 90 11 51 91 12 52 92
3 13 53 14 54 15 55 16 56
4 17 57 18 58 19 59 20 60
5 21 61 22 62 23 63 24 64
6 25 65 26 66 27 67 28 68
7 29 69 30 70 31 71 32 72
8 33 73 34 74 35 75 36 76
9 37 77 38 78 39 79 40 80


I made the ideal table like this because:
Number 1 can be in the same row with any other numbers like 5,9 or 41,81,2,42,etc.
Number 77 can be in the same row with any other numbers like 81,85,1,2,etc.
Number 2 can be in the same row with any other numbers like 1,41,77,etc.
(Looks like) only number 37 and 41 will never be in the same row.


If any number lies in the same row with its below in ideal table (say 1 in the same row with 5, 77 and 81, 78 and 82, etc) then it will have difference = 4, which I saw so many of them, as numbers in circles.
The gaps mean nothing, it's just because only 92 numbers in one table.

Thx.

 

[hopestar]

im not too sure about the placements of the numbers in a particular row. for example the number 1 is only ever found in row 0 or 1. in the first 40 tables its placed 70% of the time in row 0 and never placed 3 times consecutively in row 1. other than that it seems like its placement is completely random between these 2 rows, and i havent looked into it further.

Number 1 isn't just on row 0 or 1 as follows:
Number 93 (=1+92) on row 2 = Table 11, Table 13; on row 4 = Table 21.
Number 185 (=1+184) on row 2 = Table 7,21,22,26,36.
Thx.

 

[hopestar]

<meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 11"><meta name="Originator" content="Microsoft Word 11"><link rel="File-List" href="file:///C:%5CDOCUME%7E1%5CGATSU8%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C10%5Cclip_filelist.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <wunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <wontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style> <![endif]--> I really really appreciate your work. It has fulfilled the rule:

Number 1 won't be beneath of number 5, number 5 won't be beneath of number 9, number 9 won't be beneath of number 13, number 13 won't be beneath of number 17
Number 41 won't be beneath of number 45, number 45 won't be beneath of number 49, number 49 won't be beneath of number 53, number 53 won't be beneath of number 57.
Number 21 won't be beneath of number 25, number 25 won't be beneath of number 29, number 29 won't be beneath of number 33, number 33 won't be beneath of number 37.
Number 61 won't be beneath of number 65, number 65 won't be beneath of number 69, number 69 won't be beneath of number 73, number 73 won't be beneath of number 77.

But still breaks this:
The red & pink numbers (1,5,9,13,17,41,45,49,53,57) never touch row 9, as the dark blue & light blue numbers (21,25,29,33,37,61,65,69,73,77) never touch row 0.
But it occurs on Table 9. There’s like an ANOMALY on Table 9. Number 17 touches row 9, which on other tables number 17 is maximum touch row 8. Numbers 113,117,153 touch row 0, where they usually supposed not to be there. I don’t know for sure how it can be like that…

And not so many numbers yet in one row have difference = 4 (as numbers in circles).

Thx 3unitz for your attentions.

 

[physicslover]

<meta content=word.document name=progid><meta content="microsoft word 11" name=generator><meta content="microsoft word 11" name=originator><link href="file:///c:%5cdocume%7e1%5cgatsu8%7e1%5clocals%7e1%5ctemp%5cmsohtml1%5c10%5cclip_filelist.xml" rel=file-list><style> <!-- /* style definitions */ p.msonormal, li.msonormal, div.msonormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"times new roman"; mso-fareast-font-family:"times new roman";} @page section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.section1 {page:section1;} --> </style> i really really appreciate your work. It has fulfilled the rule:<o></o>
<o> </o>
number 1 won't be beneath of number 5, number 5 won't be beneath of number 9, number 9 won't be beneath of number 13, number 13 won't be beneath of number 17.<o></o>
number 41 won't be beneath of number 45, number 45 won't be beneath of number 49, number 49 won't be beneath of number 53, number 53 won't be beneath of number 57.<o></o>
number 21 won't be beneath of number 25, number 25 won't be beneath of number 29, number 29 won't be beneath of number 33, number 33 won't be beneath of number 37.<o></o>
number 61 won't be beneath of number 65, number 65 won't be beneath of number 69, number 69 won't be beneath of number 73, number 73 won't be beneath of number 77.<o></o>
<o> </o>
but still breaks this:
The red & pink numbers (1,5,9,13,17,41,45,49,53,57) never touch row 9, as the dark blue & light blue numbers (21,25,29,33,37,61,65,69,73,77) never touch row 0.
but it occurs on table 9. There’s like an anomaly on table 9. Number 17 touches row 9, which on other tables number 17 is maximum touch row 8. Numbers 113,117,153 touch row 0, where they usually supposed not to be there. I don’t know for sure how can it be like that…
<o> </o>
and not so many numbers yet in one row have difference = 4 (as numbers in circles).
<o> </o>
thx 3unitz for your attentions.

wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf wtf

 

[hopestar]

This is perhaps the most difficult part
Since numbers 1,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77 have made a pattern, now let’s see one table to its next table by every four numbers that following each of them as 1 2 3 4; 5 6 7 8; 9 10 11 12; … ; 89 90 91 92.

Here's an example from Table 1 to table 2:

1 2 3 4 --> 3,4 on row 2 Table 1 = 2 on row 2 Table 2 ; 2 on row 0 Table 1 = 1 on row 0 Table 2.
5 6 7 8--> 6 on row 4 Table 1 = 6 on row 4 Table 2 ; 8 on row 3 Table 1 = 7,8 on row 3 Table 2.
9 10 11 12--> no repeated number on the same row from Table 1 to Table 2.
13 14 15 16-->15 on row 6 Table 1 = 16 on row 6 Table 2 ; 16 on row 2 Table 1 = 15 on row 2 Table 2 ; 13 on row 1 Table 1 = 14 on row 1 Table 2.

Here below a table of numbers and repeated row from Table 1 to table 2 as file 1-2.psd.jpg &<o></o> from Table 2 to table 3 as file 2-3.psd.jpg :

<o></o>Conclusion:
At least there’s one number is repeated in the same row if numbers are seen by every four of them. Sometimes there’s no numbers repeated at all
Thx.

 

[hopestar]

i fixed up the code to include all the numbers (1 - 92) and to include the factors you pointed out before:

import java.util.*;
public class Table {
static Scanner console = new Scanner(System.in);
    public static void main (String[] args) 
    {
     
       String list = "010509131741454953572125293337616569737702030406070810111214" +
                     "151618192022232426272830313234353638394042434446474850515254" +
                     "5556585960626364666768707172747576787980818283848586878889909192";
       String number;
       int counter = 0;
       int randomNumber = 0;
       int rowPlacement = 0;
  
       
       Vector row_0 = new Vector();
       Vector row_1 = new Vector();
       Vector row_2 = new Vector();
       Vector row_3 = new Vector();
       Vector row_4 = new Vector();
       Vector row_5 = new Vector();
       Vector row_6 = new Vector();
       Vector row_7 = new Vector();
       Vector row_8 = new Vector();
       Vector row_9 = new Vector(); 
           
       for (counter=0; counter<184; counter = counter + 2)
       {
           number = list.substring(counter, counter + 2);
           
           //-------------------------------------------------------------------          
           if (counter == 10 || counter == 20 || counter == 30 || counter >= 40)
           {
               rowPlacement = 0;
           }
           //-------------------------------------------------------------------
           do
           {
                randomNumber = (int) ( 10 * Math.random() );   
           }
           while (rowPlacement > randomNumber);
           //-------------------------------------------------------------------
           
           if (randomNumber == 0)
           {
                row_0.addElement(number);
                rowPlacement = 0;
           }
       
           else if (randomNumber == 1)
           {
                row_1.addElement(number);
                rowPlacement = 1;
           }
       
           else if (randomNumber == 2)
           {
                row_2.addElement(number);
                rowPlacement = 2;
           }    
       
           else if (randomNumber == 3)
           {
                row_3.addElement(number);
                rowPlacement = 3;
           }
       
           else if (randomNumber == 4)
           {
                row_4.addElement(number);
                rowPlacement = 4;
           }
       
           else if (randomNumber == 5)
           {
                row_5.addElement(number);
                rowPlacement = 5;
           }
       
           else if (randomNumber == 6)
           {
                row_6.addElement(number);
                rowPlacement = 6;
           }
       
           else if (randomNumber == 7)
           {
                row_7.addElement(number);
                rowPlacement = 7;
           }
       
           else if (randomNumber == 8)
           {
                row_8.addElement(number);
                rowPlacement = 8;
           }
       
           else if (randomNumber == 9)
           {
                row_9.addElement(number);
                rowPlacement = 9;
           }
       
        }
        System.out.println(row_0);
        System.out.println(row_1);
        System.out.println(row_2);
        System.out.println(row_3);
        System.out.println(row_4);
        System.out.println(row_5);
        System.out.println(row_6);
        System.out.println(row_7);
        System.out.println(row_8);
        System.out.println(row_9);
     }
  }

heres some of the results: View attachment 18480

3unitz, how to run your code?
I tried it like this:
I've copied pasted it to Notepad++5.3 and saved it in .vb file, but when I run VB Express Edition 2008, called the file and ran it, it didn't work...
Thx.

 

[hopestar]

you have to save it as Table.java and use a java compiler

Ok, I've found the tutorial here:
http://jtute.com/java5/0000.html
I'll start learning it.
Thx.

 

[hopestar]

3unitz,
can I ask you a question?
(since I've just started learning Java) Can Java read an Excel file? If Java can, I think there should be a program for reading the worksheet of file Enigma.xls first. From there it can then trace numbers row by row from table to table (like I did manually on file 1-2.pds.jpg & 2-3.pds.jpg above) in order to find its sort of patterns. It can by then be made a correct program.
Besides, the correct program (in my imagination) has to be triggered by 'an input', so if given an input, let's say 1, the program results Table 1, if given an input 2, resulting Table2, and so on...
What do you think?
(Last night I installed the total of more than 200MB JDK5 It was so long ).
Thx.