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Clever Calculation

Age 14 to 16 Short
Challenge Level

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 $$\begin{split}2017^2-2015\times2019&=n^2-(n-2)(n+2)\\

Using just numbers
Write all the numbers in terms of $2017$, so $2015=2017-2$ and $2019=2017+2$.

ThenĀ $$\begin{split}2017^2-2015\times2019&=2017^2-(2017-2)(2017+2)\\
You can find more short problems, arranged by curriculum topic, in our short problems collection.