Twentieth Century Standard Puzzle Book / Three Parts in One Volume

by Unknown

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No. XII.—A CENTURY OF CELLS

Here is the solution of the ingenious Magic Square of 100 cells with 36 cells unfilled. The rows, columns, and diagonals all add up to 505.

91	2	3	97	6	95	94	8	9	100
20	82	83	17	16	15	14	88	89	81
21	72	73	74	25	26	27	78	79	30
60	39	38	64	66	65	67	33	32	41
50	49	48	57	55	56	54	43	42	51
61	59	58	47	45	46	44	53	52	40
31	69	68	34	35	36	37	63	62	70
80	22	23	24	75	76	77	28	29	71
90	12	13	87	86	85	84	18	19	11
1	99	98	4	96	5	7	93	92	10

Notice that the top and bottom rows contain all the numbers from 1 to 10 and from 91 to 100; the two rows next to these range from 11 to 20 and from 81 to 90; the two next from 21 to 30 and from 71 to 80; the two next from 31 to 39 and 60 to 70, excluding 61, but including 41; and the two central rows the numbers run from 42 to 59, with 40 and 61.

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No. XXIII.—TWIN PUZZLE SQUARES

The following diagram shows how the twin Magic Squares are evolved from our diagram:—

1	5	6		2	3	7
2	6	7		3	4	8
3	7	8		4	5	9

The sums of the corresponding rows in each square are now equal, and the sums of the squares of the corresponding cells of these rows are equal. The sums of the four diagonals are also equal, and the sum of the squares of the cells in corresponding diagonals are equal. The sum of any two numbers symmetrically placed with respect to the connecting link between the 7 and the 3 is always 10.