The Lily Pond

Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Once there was a rectangular lily pond. In it there were $12$ lily leaves and $6$ lily flowers.

Image
The Lily Pond

Freddie the Frog lived on one lily leaf which we will call "leaf $1$, row $4$". Sammy Snail lived on another leaf which we will call "leaf $2$, row $3$". Freddie used to jump from leaf to leaf but he did not like jumping over the lily flowers so he never jumped diagonally.

One day Freddie went to see Sammy Snail. He visited as many of the leaves as he could on the way but only visited each leaf once. Which was the best way for him to go?

If Sammy lived on a different leaf Freddie would be able to go on every leaf on his way to see Sammy. Which leaves would make this possible?