Trimagic square, 12th-order

Walter Trump (Schwabach, 1953 - )

The first known order-12 trimagic square is due to the German Walter Trump. The square was found in June 2002. He is "symmetrical" left/right: the i-th element of a row + the (13-i)th element of this same row = 12² + 1 = 145.

June 2002: First known 12th-order trimagic square,
of Walter Trump

1	22	33	41	62	66	79	83	104	112	123	144
9	119	45	115	107	93	52	38	30	100	26	136
75	141	35	48	57	14	131	88	97	110	4	70
74	8	106	49	12	43	102	133	96	39	137	71
140	101	124	42	60	37	108	85	103	21	44	5
122	76	142	86	67	126	19	78	59	3	69	23
55	27	95	135	130	89	56	15	10	50	118	90
132	117	68	91	11	99	46	134	54	77	28	13
73	64	2	121	109	32	113	36	24	143	81	72
58	98	84	116	138	16	129	7	29	61	47	87
80	34	105	6	92	127	18	53	139	40	111	65
51	63	31	20	25	128	17	120	125	114	82	94

The sums of the rows, columns and diagonals are equal to 870. The sums of the squares of the rows, columns and diagonals are equal to 83,810. The sums of the cubes of the rows, columns and diagonals are equal to 9,082,800.

• Article published in the German newspaper Schwabacher Tagblatt, October 1st 2002 (.JPG file, 120Kb)
• Article published in the German newspaper Nürnberger Nachrichten, October 29th 2002 (.JPG file, 189Kb)
• English translation of the Nürnberger Nachrichten article (Thanks to Werner Thamer for his translation)
• Story of the smallest trimagic square, text written by Walter Trump

In 2018, sixteen years later, Walter Trump worked again on 12th-order trimagic squares. Look at his webpages.

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