By Ishida Akira, James Davies

The authors lay down a couple of transparent ideas, then struggle through a wealth of examples and difficulties from expert play, providing you with a radical clutch of ways to decide on process, the way to execute dual-purpose assaults, tips on how to strength your opponent into submission or cooperation, tips to invade and decrease territorial frameworks, and whilst to struggle a ko.

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**Additional info for Attack and Defense (Elementary Go Series Vol. 5)**

**Sample text**

Reflecting on this, we realize that in the course of twelve hours the minute hand and hour hand coincide eleven times. Specifically, this happens at 12:00; at some time between 1:00 and 2:00; between 2:00 and 3:00 (we already figured this one out); between 3:00 and 4:00 (we figured this one out, too); between 4:00 and 5:00; between 5:00 and 6:00; between 41 ✐ ✐ ✐ ✐ ✐ ✐ “main” — 2008/10/2 — 18:29 — page 42 — #54 ✐ ✐ 42 2 Intermediate Problems 6:00 and 7:00; between 7:00 and 8:00; between 8:00 and 9:00; between 9:00 and 10:00; and between 10:00 and 11:00.

2 Geometry 61 In the picture, both endpoints of the line are labeled A to indicate how the triangles are cut and laid along the line. Also, the apexes of the triangles are all labeled O, since they all come from the incenter. Cut each of the three triangles into three pieces and arrange the pieces to make a rectangle of the same area. This is easy to do by cutting along the dotted lines in the diagram. Note that the altitude of each triangle (from the line) is interior to the triangle. The base of each triangle becomes the base of the corresponding rectangle.

Z/. Then R has degree at most n and has n C 1 roots, namely, ˛0 , ˛1 , . . , ˛n . Hence, R is identically 0, and P and Q are identical polynomials. This proves uniqueness. 2 Geometry What’s the Side Length? Let P be a point inside an equilateral triangle ABC , with PA D 4, PB D 3, and P C D 5. Find x, the side length of the triangle. 1 This formula is credited to Joseph-Louis Lagrange (1736–1813). Lagrange made contributions in analysis, number theory, and classical and celestial mechanics. 2 Geometry 47 C x x 5 4 P A 3 B x Solution As in the figure below, rotate 4ABC 60ı clockwise around B.