diff --git a/ch02/2.2/2.2.md b/ch02/2.2/2.2.md
index 1c16851..f7e8779 100644
--- a/ch02/2.2/2.2.md
+++ b/ch02/2.2/2.2.md
@@ -137,6 +137,9 @@ the following languages. In each case show that your grammar is correct.
     10101 is 3*7, hence, k = 7 = 111 in binary. Because 111 has more than 2
     consecutive 1's in binary, the grammar will never produce 21.
 
+   **Another proof**:
+   
+   Notice that every number generated by this grammar has a even number of 1, while 10101 has an odd number of 1. It can't be generated by this grammar.
 
 ### 2.2.6