Home | email | Knight's tour

Warnsdorff's rule results

   C     B   
 D         A 
     X     
E       H
   F   G  
  Warnsdorff's rule says that next move should go to the square with least free remaining "exits", but this often becomes a choice between more than one equally good squares. Then it matters in which order you choose to test possible "next-squares" - your priority order. There are 8! = 40320 priority orders, and to describe them, the possible "next-squares" are labelled as in the figure to the left.
Start squares are given as 'column / row'.

The amendment to Warnsdorff's rule says that if there are two or more equally good next-squares, then the square which is farthest away from the centre of the board should be chosen. But this amendment does not resolve all ambiguities. When, for instance, the current square is on the symmetry axis of the board, then the possible next-squares are pairwise equidistant from board centre. So the following gives examples of just one way of applying the amendment. It could be implemented in several other ways.

This page examines the influence of the amendment and fixed priority order, on 5x5 boards to 15x15 boards from three aspects.
1. How does the amendment perform ? Will it give complete tours regardless of where the tour started, or are there squares, that when used as start squares, will cause the tour to stop in a dead end ?
2. How many of the fixed priority orders will give complete tours regardless of where the tours started ? Examples are given of
  I priority orders that will give complete tours using any square as start square,
  II the first order found that will give an incomplete tour
  III the first order found that will give the shortest tour. (there might be several equally short tours)
3. When starting from a particular square, how many fixed orders could be used to give a complete tour ?
It turns out that the risk of the tour to end incomplete when starting from a random square, ranges from 28.2 % on a 5x5 board, down to 0.78 % on a 15x15 board.

Tours from the start squares given below could rather easily be tested with the step facility of the Applet on previous page




5x5 Board

Amendment:
Complete tours: 13
Unfinished tours: 0
* On a NxN board where N is odd, it is impossible to get a complete tour when starting from a white square. So these squares are not considered.)

Fixed priority orders:
Problem free: 0  0.0 %
Problematic: 40320  100.0 %     First ex.: ABCDEFGH starting at: 1/3     Shortest: ABCDEFGH at: 1/3   - 16 moves
(There is not one priority order, which could give a complete tour starting from all squares - for every order you could find at least one square giving an incomplete tour when that square is used as start square.)

Number of unfinished tours starting from each square:
Average probability: 147840/(13*40320) ~ 28.2 %
(When starting from a corner square or from the centre square, any priority order will give a complete tours. For other squares, the number of priority orders that will cause an unfinished tour, is given in the figure below.)

5 0*20160
50.0 %		*0
4 *16800
41.7 %		*16800
41.7 %		*
3 20160
50.0 %		*0*20160
50.0 %
2 *16800
41.7 %		*16800
41.7 %		*
1 0*20160
50.0 %		*0
 12345



6x6 Board

Amendment:
Complete tours: 36
Unfinished tours: 0

Fixed priority orders:
Problem free: 25088  62.2 %     First ex.: ABCDEGHF
Problematic: 15232  37.8 %     First ex.: ABCDEFGH starting at: 4/4     Shortest: ABCDEFGH at: 4/4   - 33 moves

Number of unfinished tours starting from each square:
Average probability: 19712/(36*40320) ~ 1.4 %

6 000000
5 000000
4 004928
12.2 %		4928
12.2 %		00
3 004928
12.2 %		4928
12.2 %		00
2 000000
1 000000
 123456



7x7 Board

Amendment:
Complete tours: 9
Unfinished tours: 16, starting from 1/1 3/1 5/1 7/1 4/2 1/3 7/3 2/4 6/4 1/5 7/5 4/6 1/7 3/7 5/7 7/7 (yellow squares)

Fixed priority orders:
Problem free: 168  0.4 %     First ex.: ABDEGCHF
Problematic: 40152  99.6 %     First ex.: ABCDEFGH starting at: 2/2     Shortest: ABDFGCEH at: 2/4   - 26 moves

Number of unfinished tours starting from each square:
Average probability: 204280/(25*40320) ~ 20.3 %

7 7848
19.5 %		*8081
20.0 %		*8081
20.0 %		*7848
19.5 %
6 *4346
10.8 %		*11874
29.4 %		*4346
10.8 %		*
5 8081
20.0 %		*10700
26.5 %		*10700
26.5 %		*8081
20.0 %
4 *11874
29.4 %		*560
1.4 %		*11874
29.4 %		*
3 8081
20.0 %		*10700
26.5 %		*10700
26.5 %		*8081
20.0 %
2 *4346
10.8 %		*11874
29.4 %		*4346
10.8 %		*
1 7848
19.5 %		*8081
20.0 %		*8081
20.0 %		*7848
19.5 %
 1234567



8x8 Board

Amendment:
Complete tours: 64
Unfinished tours: 0

Fixed priority orders:
Problem free: 7376  18.3 %     First ex.: ABCDEGFH
Problematic: 32944  81.7 %     First ex.: ABCDEFGH starting at: 3/5     Shortest: ACDFBHGE at: 4/7   - 46 moves

Number of unfinished tours starting from each square:
Average probability: 78832/(64*40320) ~ 3.1 %

8 396
1.0 %		272
0.7 %		609
1.5 %		1313
3.3 %		1313
3.3 %		609
1.5 %		272
0.7 %		396
1.0 %
7 272
0.7 %		1386
3.4 %		338
0.8 %		3457
8.6 %		3457
8.6 %		338
0.8 %		1386
3.4 %		272
0.7 %
6 609
1.5 %		338
0.8 %		1080
2.7 %		1902
4.7 %		1902
4.7 %		1080
2.7 %		338
0.8 %		609
1.5 %
5 1313
3.3 %		3457
8.6 %		1902
4.7 %		1064
2.6 %		1064
2.6 %		1902
4.7 %		3457
8.6 %		1313
3.3 %
4 1313
3.3 %		3457
8.6 %		1902
4.7 %		1064
2.6 %		1064
2.6 %		1902
4.7 %		3457
8.6 %		1313
3.3 %
3 609
1.5 %		338
0.8 %		1080
2.7 %		1902
4.7 %		1902
4.7 %		1080
2.7 %		338
0.8 %		609
1.5 %
2 272
0.7 %		1386
3.4 %		338
0.8 %		3457
8.6 %		3457
8.6 %		338
0.8 %		1386
3.4 %		272
0.7 %
1 396
1.0 %		272
0.7 %		609
1.5 %		1313
3.3 %		1313
3.3 %		609
1.5 %		272
0.7 %		396
1.0 %
 12345678



9x9 Board

Amendment:
Complete tours: 41
Unfinished tours: 0

Fixed priority orders:
Problem free: 15104  37.5 %     First ex.: ABCDEFGH
Problematic: 25216  62.5 %     First ex.: ABCDEFHG starting at: 7/3     Shortest: ABDEGCFH at: 2/6   - 52 moves

Number of unfinished tours starting from each square:
Average probability: 39744/(41*40320) ~ 2.4 %

9 706
1.8 %		*757
1.9 %		*700
1.7 %		*757
1.9 %		*706
1.8 %
8 *2474
6.1 %		*899
2.2 %		*899
2.2 %		*2474
6.1 %		*
7 757
1.9 %		*1190
3.0 %		*288
0.7 %		*1190
3.0 %		*757
1.9 %
6 *899
2.2 %		*906
2.2 %		*906
2.2 %		*899
2.2 %		*
5 700
1.7 %		*288
0.7 %		*1440
3.6 %		*288
0.7 %		*700
1.7 %
4 *899
2.2 %		*906
2.2 %		*906
2.2 %		*899
2.2 %		*
3 757
1.9 %		*1190
3.0 %		*288
0.7 %		*1190
3.0 %		*757
1.9 %
2 *2474
6.1 %		*899
2.2 %		*899
2.2 %		*2474
6.1 %		*
1 706
1.8 %		*757
1.9 %		*700
1.7 %		*757
1.9 %		*706
1.8 %
 123456789



10x10 Board

Amendment:
Complete tours: 92
Unfinished tours: 8, starting from 3/2 8/2 1/5 10/5 1/6 10/6 3/9 8/9 (yellow squares)

Fixed priority orders:
Problem free: 12368  30.7 %     First ex.: ABCDEHFG
Problematic: 27952  69.3 %     First ex.: ABCDEFGH starting at: 4/2     Shortest: AHGECFDB at: 8/7   - 45 moves

Number of unfinished tours starting from each square:
Average probability: 50400/(100*40320) ~ 1.2 %

10 872
2.2 %		570
1.4 %		377
0.9 %		443
1.1 %		536
1.3 %		536
1.3 %		443
1.1 %		377
0.9 %		570
1.4 %		872
2.2 %
9 570
1.4 %		460
1.1 %		459
1.1 %		419
1.0 %		467
1.2 %		467
1.2 %		419
1.0 %		459
1.1 %		460
1.1 %		570
1.4 %
8 377
0.9 %		459
1.1 %		426
1.1 %		380
0.9 %		528
1.3 %		528
1.3 %		380
0.9 %		426
1.1 %		459
1.1 %		377
0.9 %
7 443
1.1 %		419
1.0 %		380
0.9 %		400
1.0 %		629
1.6 %		629
1.6 %		400
1.0 %		380
0.9 %		419
1.0 %		443
1.1 %
6 536
1.3 %		467
1.2 %		528
1.3 %		629
1.6 %		826
2.0 %		826
2.0 %		629
1.6 %		528
1.3 %		467
1.2 %		536
1.3 %
5 536
1.3 %		467
1.2 %		528
1.3 %		629
1.6 %		826
2.0 %		826
2.0 %		629
1.6 %		528
1.3 %		467
1.2 %		536
1.3 %
4 443
1.1 %		419
1.0 %		380
0.9 %		400
1.0 %		629
1.6 %		629
1.6 %		400
1.0 %		380
0.9 %		419
1.0 %		443
1.1 %
3 377
0.9 %		459
1.1 %		426
1.1 %		380
0.9 %		528
1.3 %		528
1.3 %		380
0.9 %		426
1.1 %		459
1.1 %		377
0.9 %
2 570
1.4 %		460
1.1 %		459
1.1 %		419
1.0 %		467
1.2 %		467
1.2 %		419
1.0 %		459
1.1 %		460
1.1 %		570
1.4 %
1 872
2.2 %		570
1.4 %		377
0.9 %		443
1.1 %		536
1.3 %		536
1.3 %		443
1.1 %		377
0.9 %		570
1.4 %		872
2.2 %
 12345678910



11x11 Board

Amendment:
Complete tours: 60
Unfinished tours: 1, starting from 1/7 (yellow square)

Fixed priority orders:
Problem free: 21392  53.1 %     First ex.: ABCDEFGH
Problematic: 18928  46.9 %     First ex.: ABCDEGFH starting at: 5/5     Shortest: AGBECFDH at: 7/7   - 58 moves

Number of unfinished tours starting from each square:
Average probability: 27176/(61*40320) ~ 1.1 %

11 272
0.7 %		*304
0.8 %		*150
0.4 %		*150
0.4 %		*304
0.8 %		*272
0.7 %
10 *490
1.2 %		*379
0.9 %		*568
1.4 %		*379
0.9 %		*490
1.2 %		*
9 304
0.8 %		*798
2.0 %		*469
1.2 %		*469
1.2 %		*798
2.0 %		*304
0.8 %
8 *379
0.9 %		*178
0.4 %		*784
1.9 %		*178
0.4 %		*379
0.9 %		*
7 150
0.4 %		*469
1.2 %		*1010
2.5 %		*1010
2.5 %		*469
1.2 %		*150
0.4 %
6 *568
1.4 %		*784
1.9 %		*360
0.9 %		*784
1.9 %		*568
1.4 %		*
5 150
0.4 %		*469
1.2 %		*1010
2.5 %		*1010
2.5 %		*469
1.2 %		*150
0.4 %
4 *379
0.9 %		*178
0.4 %		*784
1.9 %		*178
0.4 %		*379
0.9 %		*
3 304
0.8 %		*798
2.0 %		*469
1.2 %		*469
1.2 %		*798
2.0 %		*304
0.8 %
2 *490
1.2 %		*379
0.9 %		*568
1.4 %		*379
0.9 %		*490
1.2 %		*
1 272
0.7 %		*304
0.8 %		*150
0.4 %		*150
0.4 %		*304
0.8 %		*272
0.7 %
 1234567891011



12x12 Board

Amendment:
Complete tours: 144
Unfinished tours: 0

Fixed priority orders:
Problem free: 11136  27.6 %     First ex.: ABCDFGHE
Problematic: 29184  72.4 %     First ex.: ABCDEFGH starting at: 4/1     Shortest: AEDBFHGC at: 4/10   - 67 moves

Number of unfinished tours starting from each square:
Average probability: 54144/(144*40320) ~ 0.9 %

12 326
0.8 %		364
0.9 %		299
0.7 %		288
0.7 %		208
0.5 %		334
0.8 %		334
0.8 %		208
0.5 %		288
0.7 %		299
0.7 %		364
0.9 %		326
0.8 %
11 364
0.9 %		384
1.0 %		256
0.6 %		308
0.8 %		251
0.6 %		376
0.9 %		376
0.9 %		251
0.6 %		308
0.8 %		256
0.6 %		384
1.0 %		364
0.9 %
10 299
0.7 %		256
0.6 %		466
1.2 %		492
1.2 %		373
0.9 %		318
0.8 %		318
0.8 %		373
0.9 %		492
1.2 %		466
1.2 %		256
0.6 %		299
0.7 %
9 288
0.7 %		308
0.8 %		492
1.2 %		252
0.6 %		542
1.3 %		589
1.5 %		589
1.5 %		542
1.3 %		252
0.6 %		492
1.2 %		308
0.8 %		288
0.7 %
8 208
0.5 %		251
0.6 %		373
0.9 %		542
1.3 %		564
1.4 %		537
1.3 %		537
1.3 %		564
1.4 %		542
1.3 %		373
0.9 %		251
0.6 %		208
0.5 %
7 334
0.8 %		376
0.9 %		318
0.8 %		589
1.5 %		537
1.3 %		474
1.2 %		474
1.2 %		537
1.3 %		589
1.5 %		318
0.8 %		376
0.9 %		334
0.8 %
6 334
0.8 %		376
0.9 %		318
0.8 %		589
1.5 %		537
1.3 %		474
1.2 %		474
1.2 %		537
1.3 %		589
1.5 %		318
0.8 %		376
0.9 %		334
0.8 %
5 208
0.5 %		251
0.6 %		373
0.9 %		542
1.3 %		564
1.4 %		537
1.3 %		537
1.3 %		564
1.4 %		542
1.3 %		373
0.9 %		251
0.6 %		208
0.5 %
4 288
0.7 %		308
0.8 %		492
1.2 %		252
0.6 %		542
1.3 %		589
1.5 %		589
1.5 %		542
1.3 %		252
0.6 %		492
1.2 %		308
0.8 %		288
0.7 %
3 299
0.7 %		256
0.6 %		466
1.2 %		492
1.2 %		373
0.9 %		318
0.8 %		318
0.8 %		373
0.9 %		492
1.2 %		466
1.2 %		256
0.6 %		299
0.7 %
2 364
0.9 %		384
1.0 %		256
0.6 %		308
0.8 %		251
0.6 %		376
0.9 %		376
0.9 %		251
0.6 %		308
0.8 %		256
0.6 %		384
1.0 %		364
0.9 %
1 326
0.8 %		364
0.9 %		299
0.7 %		288
0.7 %		208
0.5 %		334
0.8 %		334
0.8 %		208
0.5 %		288
0.7 %		299
0.7 %		364
0.9 %		326
0.8 %
 123456789101112



13x13 Board

Amendment:
Complete tours: 82
Unfinished tours: 3, starting from 1/5 3/9 11/9 (yellow squares)

Fixed priority orders:
Problem free: 20520  50.9 %     First ex.: ABCDEFGH
Problematic: 19800  49.1 %     First ex.: ABCDEGFH starting at: 2/2     Shortest: AEGFDCBH at: 5/9   - 80 moves

Number of unfinished tours starting from each square:
Average probability: 28312/(85*40320) ~ 0.8 %

13 218
0.5 %		*290
0.7 %		*219
0.5 %		*368
0.9 %		*219
0.5 %		*290
0.7 %		*218
0.5 %
12 *476
1.2 %		*270
0.7 %		*287
0.7 %		*287
0.7 %		*270
0.7 %		*476
1.2 %		*
11 290
0.7 %		*238
0.6 %		*302
0.7 %		*178
0.4 %		*302
0.7 %		*238
0.6 %		*290
0.7 %
10 *270
0.7 %		*300
0.7 %		*402
1.0 %		*402
1.0 %		*300
0.7 %		*270
0.7 %		*
9 219
0.5 %		*302
0.7 %		*578
1.4 %		*546
1.4 %		*578
1.4 %		*302
0.7 %		*219
0.5 %
8 *287
0.7 %		*402
1.0 %		*496
1.2 %		*496
1.2 %		*402
1.0 %		*287
0.7 %		*
7 368
0.9 %		*178
0.4 %		*546
1.4 %		*560
1.4 %		*546
1.4 %		*178
0.4 %		*368
0.9 %
6 *287
0.7 %		*402
1.0 %		*496
1.2 %		*496
1.2 %		*402
1.0 %		*287
0.7 %		*
5 219
0.5 %		*302
0.7 %		*578
1.4 %		*546
1.4 %		*578
1.4 %		*302
0.7 %		*219
0.5 %
4 *270
0.7 %		*300
0.7 %		*402
1.0 %		*402
1.0 %		*300
0.7 %		*270
0.7 %		*
3 290
0.7 %		*238
0.6 %		*302
0.7 %		*178
0.4 %		*302
0.7 %		*238
0.6 %		*290
0.7 %
2 *476
1.2 %		*270
0.7 %		*287
0.7 %		*287
0.7 %		*270
0.7 %		*476
1.2 %		*
1 218
0.5 %		*290
0.7 %		*219
0.5 %		*368
0.9 %		*219
0.5 %		*290
0.7 %		*218
0.5 %
 12345678910111213



14x14 Board

Amendment:
Complete tours: 196
Unfinished tours: 0

Fixed priority orders:
Problem free: 8376  20.8 %     First ex.: ABCDEHGF
Problematic: 31944  79.2 %     First ex.: ABCDEFGH starting at: 9/7     Shortest: ABHDCFGE at: 10/5   - 102 moves

Number of unfinished tours starting from each square:
Average probability: 65600/(196*40320) ~ 0.8 %

14 372
0.9 %		262
0.6 %		231
0.6 %		297
0.7 %		281
0.7 %		304
0.8 %		313
0.8 %		313
0.8 %		304
0.8 %		281
0.7 %		297
0.7 %		231
0.6 %		262
0.6 %		372
0.9 %
13 262
0.6 %		258
0.6 %		267
0.7 %		334
0.8 %		346
0.9 %		417
1.0 %		300
0.7 %		300
0.7 %		417
1.0 %		346
0.9 %		334
0.8 %		267
0.7 %		258
0.6 %		262
0.6 %
12 231
0.6 %		267
0.7 %		318
0.8 %		290
0.7 %		260
0.6 %		330
0.8 %		333
0.8 %		333
0.8 %		330
0.8 %		260
0.6 %		290
0.7 %		318
0.8 %		267
0.7 %		231
0.6 %
11 297
0.7 %		334
0.8 %		290
0.7 %		320
0.8 %		301
0.7 %		355
0.9 %		334
0.8 %		334
0.8 %		355
0.9 %		301
0.7 %		320
0.8 %		290
0.7 %		334
0.8 %		297
0.7 %
10 281
0.7 %		346
0.9 %		260
0.6 %		301
0.7 %		446
1.1 %		454
1.1 %		466
1.2 %		466
1.2 %		454
1.1 %		446
1.1 %		301
0.7 %		260
0.6 %		346
0.9 %		281
0.7 %
9 304
0.8 %		417
1.0 %		330
0.8 %		355
0.9 %		454
1.1 %		360
0.9 %		401
1.0 %		401
1.0 %		360
0.9 %		454
1.1 %		355
0.9 %		330
0.8 %		417
1.0 %		304
0.8 %
8 313
0.8 %		300
0.7 %		333
0.8 %		334
0.8 %		466
1.2 %		401
1.0 %		574
1.4 %		574
1.4 %		401
1.0 %		466
1.2 %		334
0.8 %		333
0.8 %		300
0.7 %		313
0.8 %
7 313
0.8 %		300
0.7 %		333
0.8 %		334
0.8 %		466
1.2 %		401
1.0 %		574
1.4 %		574
1.4 %		401
1.0 %		466
1.2 %		334
0.8 %		333
0.8 %		300
0.7 %		313
0.8 %
6 304
0.8 %		417
1.0 %		330
0.8 %		355
0.9 %		454
1.1 %		360
0.9 %		401
1.0 %		401
1.0 %		360
0.9 %		454
1.1 %		355
0.9 %		330
0.8 %		417
1.0 %		304
0.8 %
5 281
0.7 %		346
0.9 %		260
0.6 %		301
0.7 %		446
1.1 %		454
1.1 %		466
1.2 %		466
1.2 %		454
1.1 %		446
1.1 %		301
0.7 %		260
0.6 %		346
0.9 %		281
0.7 %
4 297
0.7 %		334
0.8 %		290
0.7 %		320
0.8 %		301
0.7 %		355
0.9 %		334
0.8 %		334
0.8 %		355
0.9 %		301
0.7 %		320
0.8 %		290
0.7 %		334
0.8 %		297
0.7 %
3 231
0.6 %		267
0.7 %		318
0.8 %		290
0.7 %		260
0.6 %		330
0.8 %		333
0.8 %		333
0.8 %		330
0.8 %		260
0.6 %		290
0.7 %		318
0.8 %		267
0.7 %		231
0.6 %
2 262
0.6 %		258
0.6 %		267
0.7 %		334
0.8 %		346
0.9 %		417
1.0 %		300
0.7 %		300
0.7 %		417
1.0 %		346
0.9 %		334
0.8 %		267
0.7 %		258
0.6 %		262
0.6 %
1 372
0.9 %		262
0.6 %		231
0.6 %		297
0.7 %		281
0.7 %		304
0.8 %		313
0.8 %		313
0.8 %		304
0.8 %		281
0.7 %		297
0.7 %		231
0.6 %		262
0.6 %		372
0.9 %
 1234567891011121314



15x15 Board

Amendment:
Complete tours: 111
Unfinished tours: 2, starting from 1/13 1/15 (yellow squares)

Fixed priority orders:
Problem free: 17712  43.9 %     First ex.: ABCDEGFH
Problematic: 22608  56.1 %     First ex.: ABCDEFGH starting at: 10/2     Shortest: AHDFBECG at: 8/6   - 112 moves

Number of unfinished tours starting from each square:
Average probability: 35480/(113*40320) ~ 0.8 %

15 226
0.6 %		*219
0.5 %		*183
0.5 %		*268
0.7 %		*268
0.7 %		*183
0.5 %		*219
0.5 %		*226
0.6 %
14 *246
0.6 %		*226
0.6 %		*270
0.7 %		*344
0.9 %		*270
0.7 %		*226
0.6 %		*246
0.6 %		*
13 219
0.5 %		*328
0.8 %		*330
0.8 %		*302
0.7 %		*302
0.7 %		*330
0.8 %		*328
0.8 %		*219
0.5 %
12 *226
0.6 %		*306
0.8 %		*312
0.8 %		*254
0.6 %		*312
0.8 %		*306
0.8 %		*226
0.6 %		*
11 183
0.5 %		*330
0.8 %		*462
1.1 %		*587
1.5 %		*587
1.5 %		*462
1.1 %		*330
0.8 %		*183
0.5 %
10 *270
0.7 %		*312
0.8 %		*530
1.3 %		*312
0.8 %		*530
1.3 %		*312
0.8 %		*270
0.7 %		*
9 268
0.7 %		*302
0.7 %		*587
1.5 %		*378
0.9 %		*378
0.9 %		*587
1.5 %		*302
0.7 %		*268
0.7 %
8 *344
0.9 %		*254
0.6 %		*312
0.8 %		*360
0.9 %		*312
0.8 %		*254
0.6 %		*344
0.9 %		*
7 268
0.7 %		*302
0.7 %		*587
1.5 %		*378
0.9 %		*378
0.9 %		*587
1.5 %		*302
0.7 %		*268
0.7 %
6 *270
0.7 %		*312
0.8 %		*530
1.3 %		*312
0.8 %		*530
1.3 %		*312
0.8 %		*270
0.7 %		*
5 183
0.5 %		*330
0.8 %		*462
1.1 %		*587
1.5 %		*587
1.5 %		*462
1.1 %		*330
0.8 %		*183
0.5 %
4 *226
0.6 %		*306
0.8 %		*312
0.8 %		*254
0.6 %		*312
0.8 %		*306
0.8 %		*226
0.6 %		*
3 219
0.5 %		*328
0.8 %		*330
0.8 %		*302
0.7 %		*302
0.7 %		*330
0.8 %		*328
0.8 %		*219
0.5 %
2 *246
0.6 %		*226
0.6 %		*270
0.7 %		*344
0.9 %		*270
0.7 %		*226
0.6 %		*246
0.6 %		*
1 226
0.6 %		*219
0.5 %		*183
0.5 %		*268
0.7 %		*268
0.7 %		*183
0.5 %		*219
0.5 %		*226
0.6 %
 123456789101112131415






© 2005 Gunno Törnberg
Visitors: