Trimagic square

From Wikipedia, the free encyclopedia

In mathematics, a trimagic square is a magic square that also remains magic if all of the numbers it contains are squared or cubed. Trimagic squares of orders 12, 32, 64, 81 and 128 have been discovered so far; the only known trimagic square of order 12, given below, was found in June 2002 by German mathematician 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

[edit] See also

• Magic square
• Bimagic square
• Multimagic square
• Magic cube
• Bimagic cube
• Trimagic cube
• Multimagic cube