Update usaco-737.mdx

solutions/bronze/usaco-737.mdx

@@ -2,20 +2,32 @@
 id: usaco-737
 source: USACO Bronze 2017 US Open
 title: Modern Art
-author: Juheon Rhee, Kevin Sheng, Yifan Ma
+author: Juheon Rhee, Kevin Sheng, Yifan Ma, Arnav Gokhale
 ---
 
-<Spoiler title="Hint">
+[Official Analysis (C++)](http://www.usaco.org/current/data/sol_art_bronze_open17.html)
+
+# Solution
+
+<Spoiler title="Hint 1">
 
 Try solving the sample input by hand: could you apply a similar method in your code?
 
 </Spoiler>
 
-[Official Analysis (C++)](http://www.usaco.org/current/data/sol_art_bronze_open17.html)
+<Spoiler title="Hint 2">
 
-# Solution
+What is a property of a color that cannot be the first painted?
 
-<Spoiler title="Solution">
+</Spoiler>
+
+## Explanation
+
+Firstly, notice that if two colors are overlapping, we know at least one of them cannot be the original rectangle.
+
+For each color $c_1$, we can determine the limits of that color and consider it's bounding rectangle. Any other color $c_2$ that appears inside this rectangle in the final grid mutst have been painted after $c_1$, and we can rule out $c_2$ as the first color painted.
+
+We must notice that we always choose the smallest bounding rectangle as possible for each color $c_1$. This is because a larger rectangle creates more intersection between colors, which could elminate valid starting colors.
 
 ## Implementation
 
@@ -192,5 +204,3 @@ print(sum(valid_start), file=open("art.out", "w"))
 
 </PySection>
 </LanguageSection>
-
-</Spoiler>