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Nicola's Jigsaw

Age 11 to 14 Challenge Level:

Five 3D jigsaw pieces made from multilink

Nicola has a three dimensional puzzle made from cubes.
  • There are six pieces altogether, but unfortunately one has gone missing
  • All six pieces are different shapes
  • The pieces fit together to make a 3 by 3 by 3 cube
Here are diagrams showing five of the pieces:

Three small cubes joined in a line  Five small cubes, four joined in a square and a fifth sticking out in the same plane (or a row of two on top of a row of three)  Eight cubes forming a two by two by two cube
Three cubes joined in an L shape  A line of two cubes horizontally, joined to the left of the base of a tower of two cubes stacked vertically. 

Can you figure out what shape the sixth piece is?

Is there more than one possible shape that the sixth piece could be? 

You may wish to use multilink cubes like the ones shown in the photo to help you solve the problem.

Many thanks to Nicola Coe who created the original task on which this problem is based.