http://www.azspcs.net/Contest/MagicWater

Zimmermann’s contest in March 2010 was to find the maximum water retention for magic squares orders 4 – 28.

The contest demonstrates that magic squares of any order can be produced and manipulated to explore their physical properties. ( see link above )

The solutions below are data from the final results page of the contest ..

Order 10 Magic Square Maximum Retention


1	41	79	58	75	63	64	68	52	4	505
47	80	5	81	8	90	87	6	76	25	505
78	7	35	23	97	44	36	100	13	72	505
60	82	19	91	39	29	27	14	93	51	505
73	21	98	32	40	48	33	59	16	85	505
65	89	46	26	50	62	34	30	20	83	505
56	88	43	28	31	37	22	42	92	66	505
70	11	99	17	55	38	45	94	9	67	505
53	71	12	95	24	10	96	18	77	49	505
2	15	69	54	86	84	61	74	57	3	505

505	505	505	505	505	505	505	505	505	505

( James J Youlton Jr 12 April 2010 2267 units retained)


1	42	73	56	83	61	79	80	27	3	505
49	74	17	92	20	98	8	12	82	53	505
72	4	99	16	23	22	93	50	81	45	505
59	87	19	33	40	41	48	100	7	71	505
85	14	28	29	54	65	43	32	91	64	505
60	89	35	38	66	47	39	34	11	86	505
70	9	97	62	37	36	30	21	88	55	505
51	78	46	94	24	25	18	96	5	68	505
52	77	15	10	95	26	90	13	69	58	505
6	31	76	75	63	84	57	67	44	2	505

505	505	505	505	505	505	505	505	505	505

(solution above 2^nd pattern Frederic van der Plancke 19 May 2010 2267 units retained )

10 x 10 Magic Square Water Retention

( data from Zimmermann’s contest )

Order 7 Magic Square Maximum Retention

(solution above Hermann Jurksch 6 April 2010 418 units retained

I show below my attempt to find the pattern and solution for maximum retention for the 7 x 7 magic square. I tried to find the pattern for maximum retention with a very limited number range … ie 0 to 1 using Walter Trump’s program,

0	0	1	0	1	1	0
0	1	0	1			1
1	0	0	0	1		1
0	1	0	1	0	1	0
1	0	1	0	0	0	1
1	0	0	1	0	1	0
0	1	1	0	1	0	0

Using the pattern above I was able to put the largest numbers around the largest bodies of water …. Noted below.

	25	46		31	32
27	44		45			29
47				48		30
21	43		42		41	22
33		49				40
34			37		39	28
	35	36		38	26

The F1 compiler could then search for the best solution to fill in the rest of the square. 405 units was the best result I could produce with this method.

4	25	46	19	31	32	18
27	44	16	45	12	2	29
47	10	14	6	48	20	30
21	43	1	42	5	41	22
33	11	49	3	24	15	40
34	7	13	37	17	39	28
9	35	36	23	38	26	8

My effort getting this result gave me a sincere appreciation for Hermann Jurksch’s pattern with 418 units retained.

Order 8 Magic Square Maximum Retention

(solution above Hermann Jurksch 5 April 2010 797 units retained )

Order 9 Magic Square Maximum Retention

(solution above Walter Trump 12 June 2010 1408 units retained )

Order 11 Magic Square Maximum Retention

( solution above Hugo Pfoertner 22 April 2010 3492 units retained )

( 2^nd pattern Frederic van der Plancke May 27, 2010 3492 units retained )

Order 12 Magic Square Maximum Retention

( solution above Hermann Jurksch 10 June 2010 5185 units retained )

Order 13 Magic Square Maximum Retention

(solution above Walter Trump 5 May 2010 7442 units retained )

(solution above Walter Trump 7445 units retained )

Order 14 Magic Square Maximum Retention

( solution above Frederic van der Plancke 19 May 2010 10397 units retained

Order 15 Magic Square Maximum Retention

( solution above James J Youlton Jr 15 April 2010 14154 units retained )

Below are examples for 28 x 28 Magic square … Zimmermann’s contest

213598 units retained

208913 units retained

208016 units retained

215426 units retained

197847 units retained

196165 units retained

Jarek Wroblewski 28 x 28 Magic Square Maximum retention

March 24, 2010

219822 units retained … pattern and solution below

http://tech.groups.yahoo.com/group/AlZimmermannsProgrammingContests/

The link above directs one to the discussion group section of Zimmermann’s contest. The following information can be found there

Jarek Wroblewski gives a short account of his visualization of what the pattern for maximum retention should be as well as his rules and mechanics for constructing the larger order squares. Frederic van der Plancke as well as others explain their winning strategies. Walter Trump’s programs dealing with this topic prior to the contest are available in the download section

Records are meant to be broken


1	41	79	58	75	63	64	68	52	4	505
47	80	5	81	8	90	87	6	76	25	505
78	7	35	23	97	44	36	100	13	72	505
60	82	19	91	39	29	27	14	93	51	505
73	21	98	32	40	48	33	59	16	85	505
65	89	46	26	50	62	34	30	20	83	505
56	88	43	28	31	37	22	42	92	66	505
70	11	99	17	55	38	45	94	9	67	505
53	71	12	95	24	10	96	18	77	49	505
2	15	69	54	86	84	61	74	57	3	505

505	505	505	505	505	505	505	505	505	505

4	25	46	19	31	32	18
27	44	16	45	12	2	29
47	10	14	6	48	20	30
21	43	1	42	5	41	22
33	11	49	3	24	15	40
34	7	13	37	17	39	28
9	35	36	23	38	26	8


1	41	79	58	75	63	64	68	52	4	505
47	80	5	81	8	90	87	6	76	25	505
78	7	35	23	97	44	36	100	13	72	505
60	82	19	91	39	29	27	14	93	51	505
73	21	98	32	40	48	33	59	16	85	505
65	89	46	26	50	62	34	30	20	83	505
56	88	43	28	31	37	22	42	92	66	505
70	11	99	17	55	38	45	94	9	67	505
53	71	12	95	24	10	96	18	77	49	505
2	15	69	54	86	84	61	74	57	3	505

505	505	505	505	505	505	505	505	505	505

4	25	46	19	31	32	18
27	44	16	45	12	2	29
47	10	14	6	48	20	30
21	43	1	42	5	41	22
33	11	49	3	24	15	40
34	7	13	37	17	39	28
9	35	36	23	38	26	8


1	41	79	58	75	63	64	68	52	4	505
47	80	5	81	8	90	87	6	76	25	505
78	7	35	23	97	44	36	100	13	72	505
60	82	19	91	39	29	27	14	93	51	505
73	21	98	32	40	48	33	59	16	85	505
65	89	46	26	50	62	34	30	20	83	505
56	88	43	28	31	37	22	42	92	66	505
70	11	99	17	55	38	45	94	9	67	505
53	71	12	95	24	10	96	18	77	49	505
2	15	69	54	86	84	61	74	57	3	505

505	505	505	505	505	505	505	505	505	505

4	25	46	19	31	32	18
27	44	16	45	12	2	29
47	10	14	6	48	20	30
21	43	1	42	5	41	22
33	11	49	3	24	15	40
34	7	13	37	17	39	28
9	35	36	23	38	26	8