### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

### Delia's Routes

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

# The Lily Pond

## The Lily Pond

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

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?

### Why do this problem?

This problem can be a useful introduction to the idea of coordinates. It lends itself to working together in a systematic way.

### Key questions

Where could Freddie go from here?
Can you find another way for Freddie to go?
How will you keep track of Freddie's jumps?
Can you find another place for Sammy to go so that Freddie jumps on all the leaves?

### Possible extension

Children who are familiar with the coordinate system might like to try the Treasure Island problem.

### Possible support

Some learners will find it helpful to have a copy of the picture and to draw routes onto it.