How To Find The Formula of This Permutations?

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 more than 1 MB, 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 lying 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.

RoundTower

your English is good enough but the problem still isn't very clear to me.

Perhaps you could try uploading your spreadsheet to www.rapidshare.com, although it may take quite a long time to upload an infinitely large spreadsheet.

LeixlipRed

Surely an infinitely long spread sheet would be of infinite file size?

hopestar

Hi RoundTower & LeixlipRed,
Ok, this is the link where I put the file at Rapidshare:
http://rapidshare.com/files/217674501/Enigma.xls.html
Or at Mediafire.com:
http://www.mediafire.com/?sharekey=12a93ace84ea3ab56b21be4093fab7ace04e75f6e8ebb871
Infinite amount of tables I meant there are Table 1, Table 2, Table 3,..., Table 100, Table 101, etc.
Thx.

RoundTower

LeixlipRed wrote: »

Surely an infinitely long spread sheet would be of infinite file size?

not if it's zipped using an infinitely efficient compression algorithm.

RoundTower

OK I downloaded but I still don't get it.

hopestar

Hi RoundTower,
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..??
Thx.

hopestar

Someone has made a program in Java like this:

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);
}
}

But it didn't work correctly yet

weiss

there is a good article on permutations here

not sure if that helps.

hopestar

Hi weiss,
I've seen it.
Thx for your attention.

weiss

all i can see so far is that some of the circled values are incremented in steps of 4..

are you allowed to re-arrange numbers or just fill in the blanks?

hopestar

weiss wrote: »

are you allowed to re-arrange numbers or just fill in the blanks?

I'm not so sure about your question. Perhaps this is my answer:
Yes, numbers in one row (in each tables) can be re-arranged, but can't across rows. Then fill in the blank Table 41,42,43,etc if you have found its sort of patterns.
Thx.