Warm-Up: Georgian

src/Advanced/Intro to Proofs/main.tex

@@ -1,7 +1,7 @@
 % use [nosolutions] flag to hide solutions.
 % use [solutions] flag to show solutions.
 \documentclass[
-	nosolutions,
+	solutions,
 	singlenumbering
 ]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}

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

@@ -0,0 +1,62 @@
+#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

@@ -0,0 +1,6 @@
+[metadata]
+title = "Georgian Countries"
+
+[publish]
+handout = true
+solutions = true

src/Warm-Ups/Pairs/main.typ

@@ -0,0 +1,11 @@
+#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 draw $n$ nonintersecting lines between pairs of points of different colors.

src/Warm-Ups/Pairs/meta.toml

@@ -0,0 +1,6 @@
+[metadata]
+title = "Pairs"
+
+[publish]
+handout = true
+solutions = false

src/Warm-Ups/Snakes/main.typ

@@ -76,14 +76,14 @@ All integrals are of the form $integral_a^b 1 #h(1mm) d x$.
 
 
   #v(5mm)
-  Finally, use this recusion to find that
+  Finally, use this recursion to find that
   $f_0, f_1, ..., f_7 = 1, 0, -1, -4, -13, -40, -121, -364$
 
   One can also find an explicit formula for $g_n$:
 
   $
     f_(n+1) = g_n & = x + y + 3^n c + 3^0 + 3^1 + ... + 3^n \
-                  & = x + y + 3^n c + sum_(i=0)^n 3^i       \
+                  & = x + y + 3^n c + sum_(i=0)^n 3^i \
                   & = x + y + 3^n c + (3^(n+1) + 1)/2
   $
 ]