Copyright © University of Cambridge. All rights reserved.
'From Point to Point' printed from https://nrich.maths.org/
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.