Warm-Up: Georgian

src/Warm-Ups/Pairs/main.typ

@@ -8,4 +8,17 @@
 
 #problem()
 $n$ black and $n$ white points are randomly distributed on a plane. No three points are collinear.\
-Show that it is always possible draw $n$ nonintersecting lines between pairs of points of different colors.
+Show that it is always possible to draw $n$ nonintersecting lines between pairs of points of different colors.
+
+#solution([
+  Consider the total length of all lines on the plane.
+
+  #v(2mm)
+
+  If we replace a pair of intersecting lines with two nonintersecting lines, \
+  we strictly decrease this total length (by the triangle inequality).
+
+  #v(2mm)
+  Thus, the arrangement of lines with the minimum total length must not have any intersections. \
+  Showing that a minimum exists is fairly easy.
+])