Warm-Up: Georgian

src/Warm-Ups/IOL Georgia/main.typ

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+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.4.2"
+
+#show: handout.with(
+  title: [Warm-Up: Georgian Countries],
+  by: "Mark",
+)
+
+#problem()
+There are names of some countries in South America, written in the Georgian language, together
+with their translations to English:
+
+- Brasil: ბრაზილია
+- Uruguay: ურუგვაი
+- Peru: პერუ
+
+
+What are the names, in English, of the following untranslated countries?
+
+- არგენტინა
+- კოლუმბია
+
+
+#solution[
+  - არგენტინა: Argentina
+  - კოლუმბია: Columbia
+
+  #v(4mm)
+
+  Note that "Peru" and "Uruguay" in Georgian have the same amount of characters as their translations.
+  The repetition of U in Uruguay assures us that Georgian is written left-to-right.
+
+  "Brazil" has more letters than the version in English but thanks to the two other names, we already know some letters:
+
+  #align(
+    center,
+    `_ R A _ I _ I A`,
+  )
+
+  #v(4mm)
+
+  This should probably be “Brasilia” or “Brazilia”. \
+  With those letters, we can guess the names of the other two countries:
+
+  #v(4mm)
+
+
+  #align(
+    center,
+    `A R G E _ _ I _ A`,
+  )
+
+  #align(
+    center,
+    `_ _ L U _ B I A`,
+  )
+
+  #v(4mm)
+
+
+  which can only be Argentina and Colombia (Columbia).
+]

src/Warm-Ups/IOL Georgia/meta.toml

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+[metadata]
+title = "Georgian Countries"
+
+[publish]
+handout = true
+solutions = true

src/Warm-Ups/Pairs/main.typ

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+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.4.2"
+
+#show: handout.with(
+  title: [Warm-Up: Pairs],
+  by: "Mark",
+)
+
+#problem()
+$n$ black and $n$ white points are randomly distributed on a plane. No three points are collinear.\
+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.
+])

src/Warm-Ups/Pairs/meta.toml

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+[metadata]
+title = "Pairs"
+
+[publish]
+handout = true
+solutions = false