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#1 2009-04-05 00:29:02
- wustvn
- Member
- Registered: 2007-09-23
- Posts: 8
How To Find The Formula Of This Permutations?
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 cant attach .xls file, I don't know how to put the file, name Enigma.xls.
There are infinite amount of tables (Table 1, Table 2, Table 3,
, Table 100, Table 101, etc), 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 43 (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.
Last edited by wustvn (2009-04-05 00:32:09)
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#2 2009-04-05 04:32:25
- integer
- Member
- Registered: 2008-02-21
- Posts: 79
Re: How To Find The Formula Of This Permutations?
I do not understand what you are trying to explain.
You can export the excel spreadsheet to a ".txt" or better to a ".csv" file and then include it
in your message as plain text.
This is what I have done below.
There are infinite amount of tables (Table 1, Table 2, Table 3, , Table 100, Table 101, etc), 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 43 (supposed the ideal table was right), then how to find the formulas of its permutations?
Can somebody help me about this?
These tables are truncated on the right (so that that fit on one line of this page).
Question: How is Table 1 supposed to differ from table 2.
Infinite number of tables?
It looks as if you only have 920 numbers with which to work ( 10 rows * 92 = 920)
Table 1
0 1 2 3 4 5 6 7 8
1 93 94 95 96 97 98 99 100
2 185 186 187 188 189 190 191 192
3 277 278 279 280 281 282 283 284
4 369 370 371 372 373 374 375 376
5 461 462 463 464 465 466 467 468
6 553 554 555 556 557 558 559 560
7 645 646 647 648 649 650 651 652
8 737 738 739 740 741 742 743 744
9 829 830 831 832 833 834 835 836No numbers are repeated horizontall, vertically nor diagonally.
How is this to be constructed differenly from Table 1
Table 2
0 1 2 3 4 5 6 7 8
1 93 94 95 96 97 98 99 100
2 185 186 187 188 189 190 191 192
3 277 278 279 280 281 282 283 284
4 369 370 371 372 373 374 375 376
5 461 462 463 464 465 466 467 468
6 553 554 555 556 557 558 559 560
7 645 646 647 648 649 650 651 652
8 737 738 739 740 741 742 743 744
9 829 830 831 832 833 834 835 836How is this to be form that is different from Table 1 and Table 2?
Table 3
0 1 2 3 4 5 6 7 8
1 93 94 95 96 97 98 99 100
2 185 186 187 188 189 190 191 192
3 277 278 279 280 281 282 283 284
4 369 370 371 372 373 374 375 376
5 461 462 463 464 465 466 467 468
6 553 554 555 556 557 558 559 560
7 645 646 647 648 649 650 651 652
8 737 738 739 740 741 742 743 744
9 829 830 831 832 833 834 835 836Tables 4 thorough Table 16384
How are they to be generated?
Give a example or more detailed clues.
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#3 2009-04-22 01:50:55
- wustvn
- Member
- Registered: 2007-09-23
- Posts: 8
Re: How To Find The Formula Of This Permutations?
Hi integer,
I'm so sorry for being late to answer you, because there's no notification to my e-mail.
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 = "010509131721252933374145495357616569737702030406070810111214" +
"151618192022232426272830313234353638394042434446474850515254" +
"5556585960626364666768707172747576787980818283848586878889909192";
String number;
int counter = 0;
int counter2 = 0;
int randomNumber = 0;
Vector row_selection = new Vector();
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 (counter2=0; counter2<40;)
{
//-----------------------------------------------------------------------
for (counter=0; counter<10; counter++)
{
do{randomNumber = (int) (10 * Math.random());}
while(randomNumber == 10);
row_selection.addElement(randomNumber);
}
//-----------------------------------------------------------------------
for (counter=0; counter<10;)
{
number = list.substring(counter2, counter2 + 2);
if (row_selection.indexOf(counter) != -1)
{
if (counter2 >= 20 && counter2 <30)
{
switch (counter)
{
case 0:
if(row_0.indexOf("21",0) != -1)
{
row_0.insertElementAt(number, (row_0.indexOf("21",0)));
}
else
{
row_0.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 1:
if(row_1.indexOf("21",0) != -1)
{
row_1.insertElementAt(number, (row_1.indexOf("21",0)));
}
else if (row_1.indexOf("25",0) != -1)
{
row_1.insertElementAt(number, (row_1.indexOf("25",0)));
}
else if (row_1.indexOf("29",0) != -1)
{
row_1.insertElementAt(number, (row_1.indexOf("29",0)));
}
else if (row_1.indexOf("33",0) != -1)
{
row_1.insertElementAt(number, (row_1.indexOf("33",0)));
}
else if (row_1.indexOf("37",0) != -1)
{
row_1.insertElementAt(number, (row_1.indexOf("37",0)));
}
else
{
row_1.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 2:
if(row_2.indexOf("21",0) != -1)
{
row_2.insertElementAt(number, (row_2.indexOf("21",0)));
}
else if (row_2.indexOf("25",0) != -1)
{
row_2.insertElementAt(number, (row_2.indexOf("25",0)));
}
else if (row_2.indexOf("29",0) != -1)
{
row_2.insertElementAt(number, (row_2.indexOf("29",0)));
}
else if (row_2.indexOf("33",0) != -1)
{
row_2.insertElementAt(number, (row_2.indexOf("33",0)));
}
else if (row_2.indexOf("37",0) != -1)
{
row_2.insertElementAt(number, (row_2.indexOf("37",0)));
}
else
{
row_2.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 3:
if(row_3.indexOf("21",0) != -1)
{
row_3.insertElementAt(number, (row_3.indexOf("21",0)));
}
else if (row_3.indexOf("25",0) != -1)
{
row_3.insertElementAt(number, (row_3.indexOf("25",0)));
}
else if (row_3.indexOf("29",0) != -1)
{
row_3.insertElementAt(number, (row_3.indexOf("29",0)));
}
else if (row_3.indexOf("33",0) != -1)
{
row_3.insertElementAt(number, (row_3.indexOf("33",0)));
}
else if (row_3.indexOf("37",0) != -1)
{
row_3.insertElementAt(number, (row_3.indexOf("37",0)));
}
else
{
row_3.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 4:
if(row_4.indexOf("21",0) != -1)
{
row_4.insertElementAt(number, (row_4.indexOf("21",0)));
}
else if (row_4.indexOf("25",0) != -1)
{
row_4.insertElementAt(number, (row_4.indexOf("25",0)));
}
else if (row_4.indexOf("29",0) != -1)
{
row_4.insertElementAt(number, (row_4.indexOf("29",0)));
}
else if (row_4.indexOf("33",0) != -1)
{
row_4.insertElementAt(number, (row_4.indexOf("33",0)));
}
else if (row_4.indexOf("37",0) != -1)
{
row_4.insertElementAt(number, (row_4.indexOf("37",0)));
}
else
{
row_4.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 5:
if(row_5.indexOf("21",0) != -1)
{
row_5.insertElementAt(number, (row_5.indexOf("21",0)));
}
else if (row_5.indexOf("25",0) != -1)
{
row_5.insertElementAt(number, (row_5.indexOf("25",0)));
}
else if (row_5.indexOf("29",0) != -1)
{
row_5.insertElementAt(number, (row_5.indexOf("29",0)));
}
else if (row_5.indexOf("33",0) != -1)
{
row_5.insertElementAt(number, (row_5.indexOf("33",0)));
}
else if (row_5.indexOf("37",0) != -1)
{
row_5.insertElementAt(number, (row_5.indexOf("37",0)));
}
else
{
row_5.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 6:
if(row_6.indexOf("21",0) != -1)
{
row_6.insertElementAt(number, (row_1.indexOf("21",0)));
}
else if (row_6.indexOf("25",0) != -1)
{
row_6.insertElementAt(number, (row_6.indexOf("25",0)));
}
else if (row_6.indexOf("29",0) != -1)
{
row_6.insertElementAt(number, (row_6.indexOf("29",0)));
}
else if (row_6.indexOf("33",0) != -1)
{
row_6.insertElementAt(number, (row_6.indexOf("33",0)));
}
else if (row_6.indexOf("37",0) != -1)
{
row_6.insertElementAt(number, (row_6.indexOf("37",0)));
}
else
{
row_6.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 7:
if(row_7.indexOf("21",0) != -1)
{
row_7.insertElementAt(number, (row_7.indexOf("21",0)));
}
else if (row_7.indexOf("25",0) != -1)
{
row_7.insertElementAt(number, (row_7.indexOf("25",0)));
}
else if (row_7.indexOf("29",0) != -1)
{
row_7.insertElementAt(number, (row_7.indexOf("29",0)));
}
else if (row_7.indexOf("33",0) != -1)
{
row_7.insertElementAt(number, (row_7.indexOf("33",0)));
}
else if (row_7.indexOf("37",0) != -1)
{
row_7.insertElementAt(number, (row_7.indexOf("37",0)));
}
else
{
row_7.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 8:
if(row_8.indexOf("21",0) != -1)
{
row_8.insertElementAt(number, (row_8.indexOf("21",0)));
}
else if (row_8.indexOf("25",0) != -1)
{
row_8.insertElementAt(number, (row_8.indexOf("25",0)));
}
else if (row_8.indexOf("29",0) != -1)
{
row_8.insertElementAt(number, (row_8.indexOf("29",0)));
}
else if (row_8.indexOf("33",0) != -1)
{
row_8.insertElementAt(number, (row_8.indexOf("33",0)));
}
else if (row_8.indexOf("37",0) != -1)
{
row_8.insertElementAt(number, (row_8.indexOf("37",0)));
}
else
{
row_8.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 9:
if(row_9.indexOf("21",0) != -1)
{
row_9.insertElementAt(number, (row_9.indexOf("21",0)));
}
else if (row_9.indexOf("25",0) != -1)
{
row_9.insertElementAt(number, (row_9.indexOf("25",0)));
}
else if (row_9.indexOf("29",0) != -1)
{
row_9.insertElementAt(number, (row_9.indexOf("29",0)));
}
else if (row_9.indexOf("33",0) != -1)
{
row_9.insertElementAt(number, (row_9.indexOf("33",0)));
}
else if (row_9.indexOf("37",0) != -1)
{
row_9.insertElementAt(number, (row_9.indexOf("37",0)));
}
else
{
row_9.addElement(number);
}
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
}
}
else{
switch (counter)
{
case 0:
row_0.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 1:
row_1.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 2:
row_2.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 3:
row_3.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 4:
row_4.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 5:
row_5.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 6:
row_6.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 7:
row_7.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 8:
row_8.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
case 9:
row_9.addElement(number);
row_selection.removeElementAt(row_selection.indexOf(counter));
counter2 = counter2 + 2;
break;
}
}
}
else {counter++;}
}
}
//-----------------------------------------------------------------------
System.out.println(" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20");
System.out.println("-------------------------------------------------------------------------------");
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("-------------------------------------------------------------------------------");
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 in order to result tables like I put at Mediafire.com (a file hosting service) name Enigma.xls:
http://www.mediafire.com/?sharekey=12a93ace84ea3ab56b21be4093fab7ace04e75f6e8ebb871
The clues can be found here:
http://community.boredofstudies.org/238/appreciating-beauty-elegance-extracurricular-topics/206286/how-find-formula-permutations.html#post4240925
Thx.
Last edited by wustvn (2009-05-06 02:24:25)
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