536 Puzzles and Curious Problems

296 Answers

next line of4, in 4 ways; and from the next parallelof3 trees, in I way-making,

in aU, 35 ways in that direction. Similarly BC and the lines parallel with it will

give 35 ways, and AC and the lines parallel with it, 35 ways. Then AD and the

two lines paraUei with it will give 3 ways, and similarly BF and CE, with their

parallels, will give 3 ways each. Hence 3 trees in a straight line may be selected

in 35 + 35 + 35 + 3 + 3 + 3 = 114 different ways. Therefore 1,330 - 114 =

1,216 must be the required number of ways of selecting three trees that wiU

form the points of a triangle.

11rI. THE CIRCLE AND DISCS

In our diagram the dotted lines represent the circumference of the red circle

and an inscribed pentagon. The center of both is C. Find D, a point equidis-

tant from A, B, and C, and with radius AD draw the circle ABC. Five discs
of this size will cover the circle if placed with their centers at D, E, F, G, and
H. If the diameter of the large circle is 6 inches, the diameter of the discs is a
little less than 4 inches, or 4 inches "to the nearest half-inch." It requires a
little care and practice correctly to place the five discs without shifting, unless
you make some secret markings that would not be noticed by others.