Twentieth Century Standard Puzzle Book / Three Parts in One Volume

by Unknown

No. XXIX.—MAGIC CIRCLE OF CIRCLES

We have had some good specimens of Magic Squares. Here is a very curious and most interesting Magic Circle, in which particular numbers, from 12 to 75 inclusive, are arranged in 8 concentric circular spaces and in 8 radiating lines, with the central 12 common to them all.

								62	73
								24	15
								71	64
								17	22
								69	66
								19	20
								60	75
								26	13
57	31	48	38	50	36	59	29	12		74	12	67	21	65	23	72	14
46	40	55	33	53	35	44	42			16	27	68	18	70	16	63	25
								45	58
								43	28
								52	51
								34	37
								54	49
								32	39
								47	56
								41	30

The sum of all the numbers in any of the concentric circular spaces, with the 12, is 360, which is the number of degrees in a circle.

The sum of the numbers in each radiating line with the 12, is also 360.

The sum of the numbers in the upper or lower half of any of the circular spaces, with half of 12, is 180, the degrees of a semi-circle.

The sum of any outer or inner four of the numbers on the radiating lines, with the half of 12, is also 180.

No. XXX.—THE UNIQUE TRIANGLE

In the following triangle, if two couples of the figures on opposite sides are transposed, the sums of the sides become equal, and also the sums of the squares of the numbers that lie along the sides. Which are the figures that must be transposed?