By transposing in each triangle the figures joined by dotted lines, the nine digits run in natural sequence.

No. XXXIII.—A MAGIC HEXAGON

We have dealt with Magic Squares, Circles, and Triangles. Here is a Magic Hexagon, or a nest of Hexagons, in which the numbers from 1 to 73 are arranged about the common centre 37.

1 5 6 70 60 59 58
63 8
62 19 53 46 22 45 9
61 20 24 64
2 48 31 42 38 49 57
3 47 39 40 44 56
67 51 41 37 33 23 7
66 50 34 35 54 11
65 25 36 32 43 26 12
10 30 27 13
17 29 21 28 52 55 72
18 71
16 69 68 4 14 15 73

Each of these Hexagons always gives the same sum, when counted along the six sides, or along the six diameters which join its corners, or along the six which are at right angles to its sides. These sums are 259, 185, and 111.

23

When I am in, its four legs have no motion;
When I am out, as fish it swims the ocean.
Then, if transposed, it strides across a stream,
Or adds its quality to eyes that gleam.

[Solution]

No. XXXIV.—MAGIC HEXAGON IN A CIRCLE

Inscribe six equilateral triangles in a circle, as shown in this diagram, so as to form a regular hexagon.