##### Question 12.4.3

A squirrel buries some acorns in several holes. Lamenting that she forgot where half the acorns were last winter, she decides to use a rule to remember the locations: if one hole has the coordinates $(x,y)$, then the next hole will have the coordinates $(y-2x,kx + 3y).$ She chose these numbers carefully so that the rule would cycle through all the holes, i.e. if $(x,y)$ are the coordinates of the final hole, then the rule gives the coordinates of the first hole, and this works no matter where she chose to dig the first hole. So if the squirrel can remember the location of one of the holes, she can find all of them. But once winter comes, she has forgotten the value of $k$. What might it be? Show hint