Clever calculation
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Problem
Without using a calculator, or performing any long multiplication calculations, find the value of
This problem is taken from the World Mathematics Championships
Student Solutions
Answer: $4$
Using a symbol
Suppose we use a symbol to represent $2017$, such as $n$.
Then if $n=2017$, $2015=n-2$ and $2019=n+2$.
So
Using just numbers
Write all the numbers in terms of $2017$, so $2015=2017-2$ and $2019=2017+2$.
Then