Map Folding
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles.
Label each quarter with same letter on both sides of the paper.
![Map Folding Map Folding](/sites/default/files/styles/large/public/thumbnails/content-00-03-penta4-fig1.gif?itok=3WWmk6JZ)
How many different ways can you fold it up?
Keep track of the ways by writing down the orders of letters from the top rectangle through to the bottom rectangle.
![Map Folding Map Folding](/sites/default/files/styles/large/public/thumbnails/content-00-03-penta4-fig2.gif?itok=GCVvFYni)
Now try it with a set of six rectangles!
Have you got a system for making sure you find all the ways?
Emily (Tattingstone Primary UK) is the champion map folder. She explains:
I worked this problem out by folding the piece of paper and then writing down the sequence. I then wrote the sequence backwards as, if I turned the paper upside down, it would be the same. I kept doing this until I came up with a sequence that I had already found, and couldn't find another way to do it.
This is what I came up with: BACD, DCAB, CDBA, ABDC, DBAC, CABD, ACDB, BDCA.
So that makes eight different ways to fold the map.
Emily also worked on finding the fold sequences for the larger map and found these twelve sequences:
CBADEF, FEDABC, DEFCBA, ABCFED, EFDACB, BCADFE, DFEBCA, ACBEFD, DCFEDA, ADEFCB, DABCFE, EFCBAD.
BUT ... there are more ways than this to fold the map! Can anyone find them all?