Pictured Puzzles and Word Play / A Companion to the Twentieth Century Standard Puzzle Book - A. Cyril Pearson

No. VI.—MAGIC SQUARE BY MULTIPLICATION

Here is a magic square, in which the rows, columns, and diagonals yield the same product, 4096, by multiplication:—

128	1	32
4	16	64
8	256	2

[Image]

It will be seen that the numbers in this square, 1, 2, 4, 8, 16, 32, 64, 128, 256, are in regular progression, and 4096 is also the cube of the central 16.

No. VII.—ANOTHER BORDERED MAGIC SQUARE

Here is quite a good example of a bordered magic square of sixty-four cells:—

1	56	55	11	53	13	14	57
63	15	47	22	42	24	45	2
62	49	25	40	34	31	16	3
4	48	28	37	35	30	17	61
5	44	39	26	32	33	21	60
59	19	38	27	29	36	46	6
58	20	18	43	23	41	50	7
8	9	10	54	12	52	51	64

[Image]

It is a perfect specimen itself, and as each border is removed a fresh perfect magic square is revealed.

1	56	55	11	53	13	14	57
63	15	47	22	42	24	45	2
62	49	25	40	34	31	16	3
4	48	28	37	35	30	17	61
5	44	39	26	32	33	21	60
59	19	38	27	29	36	46	6
58	20	18	43	23	41	50	7
8	9	10	54	12	52	51	64

1	56	55	11	53	13	14	57
63	15	47	22	42	24	45	2
62	49	25	40	34	31	16	3
4	48	28	37	35	30	17	61
5	44	39	26	32	33	21	60
59	19	38	27	29	36	46	6
58	20	18	43	23	41	50	7
8	9	10	54	12	52	51	64

1	56	55	11	53	13	14	57
63	15	47	22	42	24	45	2
62	49	25	40	34	31	16	3
4	48	28	37	35	30	17	61
5	44	39	26	32	33	21	60
59	19	38	27	29	36	46	6
58	20	18	43	23	41	50	7
8	9	10	54	12	52	51	64