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When calculating $63\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as 9 and gets a result which has a difference of 432 from the correct one. Which digit does she write incorrectly? 
Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles
The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong.  Then, compare $7\times63$ and $6\times72$, so we can get the correct answer.  $69\times72-63\times72=432.$ 