Panmagic & 5x5 compact 15x15 magic square

Use 3x3 the same panmagic 5x5 square (as first grid) to construct a panmagic 15x15 and 5x5 compact square.

Construct the first row of the second grid:

The sum of the numbers of each colour is 5

The sum of the numbers of each colour is 3

Construct row 2 up to 15 by shifting the first row each time 3 places to the left.

The third grid is a reflection (rotated by a quarter and mirrored) of the second grid.

*Take 1x number from 3x3 the same panmagic 5x5 square*
1	7	13	19	25	1	7	13	19	25	1	7	13	19	25
14	20	21	2	8	14	20	21	2	8	14	20	21	2	8
22	3	9	15	16	22	3	9	15	16	22	3	9	15	16
10	11	17	23	4	10	11	17	23	4	10	11	17	23	4
18	24	5	6	12	18	24	5	6	12	18	24	5	6	12
1	7	13	19	25	1	7	13	19	25	1	7	13	19	25
14	20	21	2	8	14	20	21	2	8	14	20	21	2	8
22	3	9	15	16	22	3	9	15	16	22	3	9	15	16
10	11	17	23	4	10	11	17	23	4	10	11	17	23	4
18	24	5	6	12	18	24	5	6	12	18	24	5	6	12
1	7	13	19	25	1	7	13	19	25	1	7	13	19	25
14	20	21	2	8	14	20	21	2	8	14	20	21	2	8
22	3	9	15	16	22	3	9	15	16	22	3	9	15	16
10	11	17	23	4	10	11	17	23	4	10	11	17	23	4
18	24	5	6	12	18	24	5	6	12	18	24	5	6	12


*+ 25x number from second grid*
0	1	2	0	0	1	2	0	1	2	2	0	1	2	1
0	0	1	2	0	1	2	2	0	1	2	1	0	1	2
2	0	1	2	2	0	1	2	1	0	1	2	0	0	1
2	2	0	1	2	1	0	1	2	0	0	1	2	0	1
1	2	1	0	1	2	0	0	1	2	0	1	2	2	0
0	1	2	0	0	1	2	0	1	2	2	0	1	2	1
0	0	1	2	0	1	2	2	0	1	2	1	0	1	2
2	0	1	2	2	0	1	2	1	0	1	2	0	0	1
2	2	0	1	2	1	0	1	2	0	0	1	2	0	1
1	2	1	0	1	2	0	0	1	2	0	1	2	2	0
0	1	2	0	0	1	2	0	1	2	2	0	1	2	1
0	0	1	2	0	1	2	2	0	1	2	1	0	1	2
2	0	1	2	2	0	1	2	1	0	1	2	0	0	1
2	2	0	1	2	1	0	1	2	0	0	1	2	0	1
1	2	1	0	1	2	0	0	1	2	0	1	2	2	0


*+ 75x number from third grid*
0	0	2	2	1	0	0	2	2	1	0	0	2	2	1
1	0	0	2	2	1	0	0	2	2	1	0	0	2	2
2	1	1	0	1	2	1	1	0	1	2	1	1	0	1
0	2	2	1	0	0	2	2	1	0	0	2	2	1	0
0	0	2	2	1	0	0	2	2	1	0	0	2	2	1
1	1	0	1	2	1	1	0	1	2	1	1	0	1	2
2	2	1	0	0	2	2	1	0	0	2	2	1	0	0
0	2	2	1	0	0	2	2	1	0	0	2	2	1	0
1	0	1	2	1	1	0	1	2	1	1	0	1	2	1
2	1	0	0	2	2	1	0	0	2	2	1	0	0	2
2	2	1	0	0	2	2	1	0	0	2	2	1	0	0
0	1	2	1	1	0	1	2	1	1	0	1	2	1	1
1	0	0	2	2	1	0	0	2	2	1	0	0	2	2
2	1	0	0	2	2	1	0	0	2	2	1	0	0	2
1	2	1	1	0	1	2	1	1	0	1	2	1	1	0


*= panmagic 15x15 square*
1	32	213	169	100	26	57	163	194	150	51	7	188	219	125
89	20	46	202	158	114	70	71	152	183	139	45	21	177	208
222	78	109	65	141	172	103	134	40	91	197	128	84	15	116
60	211	167	123	54	35	161	192	148	4	10	186	217	98	29
43	74	180	156	112	68	24	155	181	137	18	49	205	206	87
76	107	63	94	175	101	132	13	119	225	126	82	38	144	200
164	170	121	52	8	189	220	146	2	33	214	195	96	27	58
72	153	184	140	66	22	178	209	115	16	47	203	159	90	41
135	61	92	198	129	110	11	117	223	79	85	36	142	173	104
193	149	30	6	187	218	99	5	31	212	168	124	55	56	162
151	182	138	19	25	176	207	88	44	75	201	157	113	69	50
14	95	196	127	83	39	145	221	77	108	64	120	171	102	133
147	3	34	215	216	97	28	59	190	166	122	53	9	165	191
210	136	17	48	204	185	86	42	73	154	160	111	67	23	179
118	224	105	81	37	143	174	80	106	62	93	199	130	131	12

This panmagic 15x15 square is also 5x5 compact.

You can use this method also to construct a 21x21 magic square (take 3x3 the same panmagic 7x7 square).

15x15, Panmagic & 5x5 compact.xls

Microsoft Excel werkblad 130.5 KB

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15x15 magic square