1. TESSELATION Professor Fiendish’s fatal fungus

2. Professor Fiendish has trapped you in his bathroom. On the floor is a huge patch of fatal fungus which is about to fire its rot spores all over the room. The only way to save yourself is to cover up the patch of fungus, not even a tiny bit must be left uncovered.

3. All you have to cover the fungus with is a set of square tiles which are all exactly the same size…

4. That was easy… Unluckily, Professor Fiendish realises it is too easy with square tiles! He takes them away and shows you some shapes like this:

5. You have to choose one of the shapes, and he will give you a set of tiles of that shape. Does it matter which shape you choose to cover the fungus with, or do you think that some shapes will not work?

6. CIRCULAR TILES

7. So which of the Professor’s shapes would work and which would not? Remember, the edges of your pattern don’t have to be neat, just as long as there are no gaps in the middle. Try the Professor’s shapes and put your results into a table. Then try some shapes of your own.

8. Yes 4 3 Yes 6 Yes 8 No 5 No 0 No 8 Yes