Point Packing


The Point Packing contest has ended. Congratulations to our winners:

Position Winner Prize
1st Hugo Pfoertner Munich, Germany Any full-size sculpture by Bathsheba Grossman from these pages:
2nd Hermann Jurksch Recklinghausen, Germany Any half-size sculpture by Bathsheba Grossman from these pages:


These are the contestants who submitted the best solution for each problem. (Problems for which the best solution was found during the first 48 hours of the contest are omitted.)

Problem Score Solver Date Achieved
15 points 115.25 Jukka Jylänki Oulu, Oulu, Finland 20 Jul 2009 18:20
Tomas Rokicki Palo Alto, California, United States 23 Jul 2009 17:21
Hugo Pfoertner Munich, Germany 27 Jul 2009 23:07
Fumi Yura Akihabara, Japan 28 Jul 2009 02:29
Hermann Jurksch Recklinghausen, Germany 28 Jul 2009 21:40
Tom Sirgedas Okemos, Michigan, United States 31 Jul 2009 20:49
Garr Godfrey Seattle, Washington, United States 18 Aug 2009 04:11
Stefan Kirchner Karlsruhe, Germany 20 Aug 2009 21:25
Klaus Nagel München, Germany 21 Aug 2009 14:53
Florian Jung Mainz, Germany 31 Aug 2009 07:27
Markus Sigg Freiburg, Germany 31 Aug 2009 19:49
Valéry Gareiss Zürich, Switzerland 5 Sep 2009 21:24
William Edwards Bräkne-Hoby, Blekinge, Sweden 21 Sep 2009 00:45
Andrea Concaro Voghera, Italy 2 Oct 2009 19:51
Roland Postle Manchester, England, United Kingdom 3 Oct 2009 21:55
16 points 138.568052930057 Tomas Rokicki Palo Alto, California, United States 14 Aug 2009 18:37
Hugo Pfoertner Munich, Germany 15 Aug 2009 05:57
Stefan Kirchner Karlsruhe, Germany 20 Aug 2009 21:19
Jukka Jylänki Oulu, Oulu, Finland 21 Aug 2009 06:20
Hermann Jurksch Recklinghausen, Germany 23 Aug 2009 09:52
Markus Sigg Freiburg, Germany 31 Aug 2009 19:50
Fred Batty Santa Clara, California, United States 10 Sep 2009 23:30
Tom Sirgedas Okemos, Michigan, United States 15 Sep 2009 02:43
Ralph Gasser Palo Alto, California, United States 20 Sep 2009 19:13
Klaus Nagel München, Germany 26 Sep 2009 10:46
17 points 162.97520661157 Tomas Rokicki Palo Alto, California, United States 15 Aug 2009 01:52
Hugo Pfoertner Munich, Germany 27 Aug 2009 08:37
Tom Sirgedas Okemos, Michigan, United States 15 Sep 2009 13:42
Hermann Jurksch Recklinghausen, Germany 17 Sep 2009 15:51
Jukka Jylänki Oulu, Oulu, Finland 4 Oct 2009 12:41
Markus Sigg Freiburg, Germany 9 Oct 2009 07:23
18 points 200.08 Tomas Rokicki Palo Alto, California, United States 4 Aug 2009 02:58
Hugo Pfoertner Munich, Germany 15 Aug 2009 06:18
Tom Sirgedas Okemos, Michigan, United States 16 Sep 2009 20:24
19 points 227.239865574459 Hugo Pfoertner Munich, Germany 6 Oct 2009 06:18
20 points 268.296611328125 Hugo Pfoertner Munich, Germany 6 Oct 2009 06:09
Hermann Jurksch Recklinghausen, Germany 7 Oct 2009 23:10
21 points 315.413223140496 Jukka Jylänki Oulu, Oulu, Finland 5 Oct 2009 18:50
22 points 356.128595123286 Hugo Pfoertner Munich, Germany 6 Oct 2009 06:20
23 points 417.843341260404 Hugo Pfoertner Munich, Germany 6 Oct 2009 06:11
24 points 467.45867768595 Hugo Pfoertner Munich, Germany 6 Oct 2009 06:23
25 points 537.870916355134 Hermann Jurksch Recklinghausen, Germany 7 Oct 2009 23:07
26 points 608.780718525455 Hugo Pfoertner Munich, Germany 8 Oct 2009 17:47


These are the best solutions received for each problem in the contest:

Problem Score Solution
2 points 0.25 (0,0), (0,1)
3 points 1.25 (0,0), (0,1), (1,2)
(0,0), (0,1), (2,0)
4 points 2.5 (0,0), (0,1), (2,0), (3,1)
(0,0), (0,1), (2,2), (3,1)
(0,0), (0,1), (1,2), (3,0)
5 points 5 (0,0), (0,2), (2,4), (3,2), (3,3)
(0,0), (0,1), (2,0), (3,3), (4,2)
(0,1), (1,0), (2,3), (2,4), (4,3)
6 points 9.28200692041523 (0,1), (0,3), (0,4), (2,6), (3,0), (4,5)
7 points 12.8125 (0,2), (0,3), (2,0), (2,3), (5,6), (6,3), (7,2)
(0,2), (0,3), (2,3), (2,6), (5,0), (6,3), (7,2)
8 points 19.234693877551 (0,0), (0,3), (1,1), (5,0), (6,5), (6,6), (8,1), (8,3)
9 points 26.6919420552286 (0,2), (0,6), (1,1), (3,0), (3,3), (4,10), (5,10), (7,2), (9,7)
10 points 35.1530612244898 (0,3), (0,7), (2,9), (2,10), (5,0), (5,2), (6,11), (8,3), (10,2), (11,3)
11 points 48.5 (0,3), (0,7), (2,4), (3,0), (6,12), (7,12), (9,6), (9,12), (10,7), (12,2), (13,8)
12 points 61.8055555555556 (0,1), (0,7), (1,1), (2,15), (3,0), (5,0), (7,15), (9,2), (9,5), (9,13), (10,12), (12,7)
13 points 74.3519619500594 (0,1), (1,11), (1,15), (3,3), (3,9), (6,0), (6,16), (9,0), (9,15), (10,15), (11,4), (13,11), (14,9)
14 points 93.4730440499671 (0,3), (0,12), (1,1), (2,7), (2,15), (4,17), (8,1), (10,12), (13,0), (14,1), (14,3), (17,6), (17,7), (17,10)
15 points 115.25 (0,4), (0,8), (0,11), (0,13), (6,2), (7,18), (9,0), (11,1), (14,10), (15,0), (16,17), (17,16), (19,4), (19,14), (20,11)
16 points 138.568052930057 (0,7), (0,14), (2,4), (4,18), (7,0), (7,1), (10,7), (12,18), (12,22), (13,17), (15,18), (19,2), (19,17), (21,4), (22,14), (23,11)
17 points 162.97520661157 (0,6), (0,14), (1,14), (2,4), (5,24), (8,9), (9,24), (10,0), (10,25), (13,0), (14,21), (16,3), (16,24), (17,22), (21,20), (22,9), (23,13)
18 points 200.08 (0,9), (0,15), (1,6), (1,7), (3,24), (5,22), (6,26), (8,6), (11,0), (15,0), (15,21), (17,27), (18,3), (23,4), (23,6), (25,11), (25,16), (26,17)
19 points 227.239865574459 (0,6), (0,14), (0,18), (0,21), (1,15), (4,2), (7,0), (8,28), (10,28), (12,26), (17,1), (18,26), (19,19), (20,15), (22,2), (22,3), (24,23), (25,21), (28,14)
20 points 268.296611328125 (0,8), (0,21), (5,23), (5,28), (6,3), (8,13), (8,31), (11,2), (11,31), (11,32), (12,30), (15,0), (15,2), (22,3), (23,30), (25,15), (27,6), (27,12), (27,26), (29,20)
21 points 315.413223140496 (0,13), (1,18), (2,8), (2,15), (2,27), (8,33), (9,2), (14,30), (14,35), (15,11), (19,0), (21,1), (23,1), (25,30), (26,23), (27,6), (30,6), (32,23), (32,27), (34,15), (34,16)
22 points 356.128595123286 (0,13), (1,10), (1,22), (1,24), (2,8), (5,10), (7,26), (7,32), (9,2), (12,6), (13,0), (14,25), (16,36), (17,36), (19,3), (22,27), (22,30), (30,3), (32,5), (33,6), (34,28), (36,21)
23 points 417.843341260404 (0,10), (0,24), (1,9), (2,30), (4,29), (6,31), (9,10), (12,0), (16,0), (16,36), (17,0), (19,39), (20,9), (24,38), (26,10), (29,21), (32,4), (32,6), (32,22), (32,34), (34,27), (36,8), (37,27)
24 points 467.45867768595 (0,13), (0,17), (0,19), (0,26), (1,13), (2,23), (7,36), (8,5), (8,37), (15,4), (18,10), (23,39), (24,31), (25,7), (27,0), (30,3), (30,25), (36,29), (36,32), (37,34), (38,9), (39,20), (40,11), (42,19)
25 points 537.870916355134 (0,12), (0,15), (0,33), (1,14), (2,35), (5,7), (10,3), (10,18), (10,31), (13,1), (16,9), (16,45), (17,0), (22,43), (22,45), (27,42), (33,35), (34,7), (37,32), (38,7), (40,11), (40,12), (40,35), (41,22), (42,19)
26 points 608.780718525455 (0,19), (0,25), (1,30), (1,34), (3,11), (4,30), (8,17), (9,5), (11,44), (12,45), (15,46), (21,0), (21,9), (21,48), (22,42), (26,11), (31,40), (34,27), (37,44), (39,34), (41,8), (43,9), (43,10), (46,16), (46,35), (48,23)


The following noteworthy solutions were received after the contest ended.

Problem Score Solver Date Solution
25 points 534.867384870036 Hugo Pfoertner
Munich, Germany		 12 Feb 2010 18:06 (0,16), (0,25), (2,13), (2,16), (3,36), (5,38), (6,7), (10,3), (11,4), (14,1), (18,0), (18,45), (19,28), (20,40), (27,3), (28,1), (31,44), (33,27), (34,34), (35,8), (36,23), (38,39), (40,9), (44,27), (45,24)
26 points 604.848248810232 Hugo Pfoertner
Munich, Germany		 22 Jan 2010 20:27 (0,15), (0,17), (2,29), (3,36), (5,9), (8,43), (9,44), (11,20), (13,2), (13,40), (19,0), (22,10), (23,0), (23,45), (25,48), (26,48), (32,2), (36,3), (37,11), (37,14), (37,32), (37,41), (38,5), (41,38), (44,11), (47,20)