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Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

A Shapely Network

Age 7 to 11 Challenge Level:

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!