Making maths: disappearing goblin

If you have worked on, Disappearing Square then you will have come across some classic problems about how space (small squares and little characters in this instance) seems to appear and disappear.

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Hallowe'en is the season for strange tales told around warm fires of things that go bump in the night, move around and even disappear.

You can have great fun making puzzles like this to amuse and confuse your family and friends - why, even your teachers. Here Adam Bishop has created a template that can be used to create your own disappearing goblins. Of course, once you have had a trial run you can be creative and use different characters or objects and vary the number of them.

As always, the important task is to try and discover and explain how this works.

You will need: Paper Thin card Pencil Ruler Coloured pencils or pens Scissors A copy of the template below, or work offline and keep this page on the screen so you can see the template.

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What to do:

1. Using the template above, draw a rectangle, Alternatively, you can print off the page (don't forget the 'printable page button at the top right of the page).
2. Use a pencil and ruler to divide the rectangle horizontally into two equal parts, as shown in the diagram by the thick black line.
3. Divide the top half of the rectangle as shown by the letters A and B. B is one quarter of the top rectangle. You don't have to write the letters in.
4. Each of the 5 lightly drawn rectangles are the spaces into which you draw one of your chosen characters.
   
   We used goblins, you might want to choose a Halloween theme.
5. It is important that you stay within and follow the space of the whole lightly drawn rectangle. If the rectangle is in both the top and bottom half then your character must be drawn across the two halves, similarly if the light rectangle is in just the top or bottom then your character must not wander into the other half of the rectangle.
6. When you have carefully drawn your characters, colour them in.
7. Keep a steady hand as you cut along the two thick lines - across the centre and to separate A from B.
8. Show your masterpiece to a friend and ask them to count the characters.
   
   Switch A and B, ask them to count again.

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