Pictured Puzzles and Word Play / A Companion to the Twentieth Century Standard Puzzle Book

by A. Cyril Pearson

No. I.—A GOOD SPECIMEN

Here is a nest of magic squares, seven of them within the four corners of one diagram:—

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

[Image]

As each border is removed a fresh magic square remains, in which the numbers in the cells of each row, column, and diagonal add up to the same sum, while each of these sums is a multiple of the central 113.

No. II.—A BORDERED DIAMOND
By G. Slater

												1
											91		117
										3		20		160
									27		25		129		65
								156		154		42		38		165
							161		15		138		36		103		26
						130		153		136		124		81		54		159
					162		147		120		69		75		135		151		52
				39		22		55		112		111		110		33		64		78
			4		152		76		57		56		62		61		63		93		7
		168		146		139		100		99		98		97		96		102		142		158
	6		21		29		45		44		43		49		48		47		133		51		104
157		80		30		88		87		86		85		84		83		82		140		90		13
	53		41		134		123		122		121		127		126		125		52		145		79
		10		132		89		74		73		72		71		70		34		16		167
			105		67		35		109		108		114		113		50		155		143
				5		116		137		60		59		58		115		17		14
					144		19		107		95		101		94		23		9
						11		106		68		46		31		148		40
							118		77		37		41		18		8
								92		38		128		24		131
									163		148		149		166
										12		130		2
											66		164
												169

[Image]

It is a perfect magic diamond as it stands, and equally perfect are the diamonds that remain when each border of cells is removed, as is indicated by the lines.