# A Shapely Network

Look at the network of shapes below:

Your challenge is to find the longest way through the network following this rule:

You can start and finish anywhere, and with any shape, as long as you follow the correct order. You may only visit each shape once but you do not have to visit them all.

Concentrate on starting from a particular edge at a time and try to record your routes carefully. Perhaps you could make a tally chart showing the shape you started on, the number of shapes or "cycles" you took and the shape you finished on. You will find that you end up going over parts of routes again for different starting points and this will speed up your investigation.

Extra hint - the route starts and ends on the same shape.

Emma, Abi and Holly from Moorfield Junior School sent us this solution:

The largest number of shapes we got was $22$. We got this by starting with the second square along on the top row. Then we went :

$1$ right

$1$ down

$2$ left

$3$ down

$2$ right

$1$ up

$1$ right

$1$ up

$1$ right

$4$ down

$4$ left

and finished at the first square on the bottom row.

Thomas at Newberries Primary School sent us a picture of the same path through the network:

I don't think it's possible to beat, but maybe you can prove me wrong!