Last week, I set the following problem - A digit reversal, which confused many people (esp if you read the solutions). A high proportion of people first gave an answer of around 960. Many even claimed that 959 is the correct answer, and gave the following justification:
Since , we can check that the last three digits of are 421 and the last three digits of are 779. Hence, the last three digits of are obtained from . Thus the answer is 959.
What is wrong with the above solution? What was the wrong assumption / misconception that was made?
(Note that I am not asking for your solutions; you can view the solution discussion for different approaches.)
Here are some questions to guide you.
1. What is the remainder when 123 is divided by 1000?
2. What is the remainder when -123 is divided by 1000?
3. What are the last three digits of 123?
4. What are the last three digits of -123?
5. What is ?
6. What is ?