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From Point to Point

Age 14 to 16 Short
Challenge Level

How can you get from $(10,66)$ to  $(20,12)$

using only integer multiples of the vectors

$\begin{pmatrix}2\\-3\end{pmatrix}$ and $\begin{pmatrix}3\\2\end{pmatrix}$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
You can find more short problems, arranged by curriculum topic, in our short problems collection.