Twentieth Century Standard Puzzle Book / Three Parts in One Volume

by Unknown

[Solution]

No. VI.—ANOTHER WAY TO MAKE A MAGIC SQUARE

Here is one of many methods by which a Magic Square of the first twenty-five numbers can readily be made.

				1
			2		6
		3	20	7	24	11
	4	16	8	25	12	4	16
5		9	21	13	5	17		21
	10	22	14	1	18	10	22
		15	2	19	6	23
			20		24
				25

This is done by first placing the figures from 1 to 25 in diagonal rows, as is shown above, and then introducing the numbers that are outside the square into it, by moving each of them five places right, left, up, or down. A Magic Square is thus formed, the numbers of which add up to 65 in lines, columns and diagonals, and with the centre and any four corresponding numbers on the borders.

No. VII.—A MONSTER MAGIC SQUARE

Here is what may indeed be called a Champion Magic Square:—

23	464	459	457	109	111	108	110	132	133	130	131	373	371	357	356	372	382	370	335	30	22
25	41	436	435	433	432	196	195	241	242	200	225	284	287	246	245	288	261	51	58	47	460
27	45	13	474	469	467	82	81	72	90	91	83	401	400	396	398	399	397	20	12	440	458
461	55	15	34	450	449	447	446	156	157	180	181	326	327	306	307	44	37	33	470	430	24
456	56	17	42	3	484	479	477	66	65	68	67	422	421	416	415	10	2	443	468	429	29
137	428	471	41	5	127	126	125	361	362	363	364	365	366	118	117	116	480	444	14	57	348
153	431	466	31	7	347	148	338	339	145	143	342	142	344	345	139	138	478	454	19	54	332
154	439	98	453	481	325	161	169	168	318	319	320	321	163	162	324	160	4	32	387	46	331
384	266	407	445	476	292	293	191	190	299	298	297	186	185	184	302	193	9	40	78	219	101
383	268	406	442	424	270	280	272	273	211	210	209	208	278	279	205	215	61	43	79	217	102
379	265	392	172	60	248	227	250	251	230	232	231	233	256	257	258	237	425	313	93	220	106
378	267	391	173	59	226	249	228	229	252	254	253	255	234	235	236	259	426	312	94	218	107
351	282	405	176	74	204	214	206	207	277	276	275	274	212	213	271	281	411	309	80	203	134
350	263	390	177	73	182	192	301	300	189	187	188	296	295	294	183	303	412	308	95	222	135
334	199	77	330	423	171	315	323	322	164	165	166	167	317	316	170	314	62	155	408	286	151
333	216	96	311	413	149	346	147	146	340	341	144	343	141	140	337	336	72	174	389	269	152
100	221	76	310	414	369	359	360	124	123	122	121	120	119	367	368	358	71	175	409	264	385
99	223	75	291	483	1	6	8	419	420	417	418	63	64	69	70	475	482	194	410	262	386
104	202	97	452	35	36	38	39	329	328	305	304	159	158	179	178	441	448	451	388	283	381
105	238	473	11	16	18	403	404	393	395	394	402	84	85	89	87	86	88	465	472	247	380
136	438	49	50	52	53	289	290	244	243	285	260	201	198	239	240	197	224	434	427	437	349
463	21	26	28	376	374	377	375	353	352	355	354	112	114	128	129	113	103	115	150	455	462

Its 484 cells form, as they are numbered, a Magic Square, in which all rows, columns, and diagonals add up to 5335, and it is no easy matter to determine in how many other symmetrical ways its key-number can be found.

When the cells outside each of the dark border lines are removed, three other perfect Magic Squares remain.