diff --git "a/IMO/md/en-IMO-2021-notes.md" "b/IMO/md/en-IMO-2021-notes.md"
--- "a/IMO/md/en-IMO-2021-notes.md"
+++ "b/IMO/md/en-IMO-2021-notes.md"
@@ -164,7 +164,7 @@ Proof. Notice that \(\angle EMB = 180^{\circ} - \angle AMB - \angle EMZ = 180^{\
 Let \(N\) be the other intersection of circles \((ACD)\) and \((DEX)\) and let \(R\) be the intersection of \(AC\) and \(BM\) .
 
 
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+![md5:79441668e3d69c644744261e71aee5b3](79441668e3d69c644744261e71aee5b3.jpeg)
   
 
 Claim — Points \(B\) , \(D\) , \(M\) , \(N\) are cyclic.  
@@ -201,7 +201,7 @@ Let \(\Gamma\) be a circle with center \(I\) , and \(ABCD\) a convex quadrilater
 
 Let \(PQR S\) be the contact points of \(\Gamma\) an \(\overline{AB}\) , \(\overline{BC}\) , \(\overline{CD}\) , \(\overline{DA}\) .  
 
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+![md5:a5dbdbfdcca3b1c6bfecd8d382a56f47](a5dbdbfdcca3b1c6bfecd8d382a56f47.jpeg)
   
 
 Claim — We have \(\triangle IQZ \cong \triangle IRT\) . Similarly, \(\triangle IPX \cong \triangle ISY\) .  
@@ -242,7 +242,7 @@ Assume for contradiction no such \(k\) exists. We will use a so- called "thresho
 
 This process takes exactly 2021 steps. Right after the \(k\) th move, we consider a situation where we color walnut \(k\) red as well, so at the \(k\) th step there are \(k\) ones. For brevity, a non- red walnut is called black. An example is illustrated below with 2021 replaced by 6.  
 
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+![md5:9b665ae68de01be864315d2765666e09](9b665ae68de01be864315d2765666e09.jpeg)
   
 
 Claim — At each step, the walnut that becomes red is between two non- red or two red walnuts.