Your task is to completely surround shapes with cut-outs of the congruent shapes. Congruent means exactly the same shape and size. You may flip them over and turn them any way you like. You must surround the original shape with as few congruent shapes as possible. Surround means there must be no edge or part of the edge not blocked in by the new congruent shapes.  NOT EVEN A CORNER CAN BE EXPOSED TO THE OUTSIDE WORLD!

For example, the diagram opposite gives the original shape as a simple rectangle:

If you want to surround it completely with congruent shapes you can do it with only 5 congruent shapes as shown.

Your task it to surround each of these shapes with congruent shapes. So for Shape 1, all the shapes used to surround it must be exactly the same size and shape as Shape 1.

There are 4 problems here!

The shapes might not fit as neatly as you would like. You may need some parts sticking out. But the goal is to surround them with as few congruent shapes as you can. I can do Shape 1 and Shape 4 with four congruent shapes, and Shapes 2 and 3 needed five. Can you do them with this few - or even fewer?

1. Can you surround each Shape with 4 or 5 congruent shapes?

2. How does your brain cope with adjusting shapes? How does it cope with frustration?

3. Did you find any of these easier or harder than the others? Why might that have been?