You have a square piece of paper and you do not know its length or width.

What is the minimum number of folds required in order for the paper to only show 1/15 of its original size, 2/15 of it's original size, 3/15 of its original size, ........, 14/15 of its original size.

Note: You do not know where one-third marks or one-fifth marks lie on this piece of paper therefore you must use folds to mark these areas. You are allowed to use folds as guides to make other folds.

Part 1 - creating 15 equal areas
Crease square ABCD along diagonal BD.

A      f4       f3       f2        f1        B

                                          s1
                                                                          
t2
                                                                       
                          o
            
t1                                                                   
              q1
                                                                        

D                                                C

Then fold into 4 quarters horizontally.
q1 is the intersection of BD with the lower quarter fold.
Crease along C-q1 to form t1 which is 1/3 from D to A.  Fold A to t1 to form t2.

Fold A to t2 and crease to form s1 on BD.  Crease C-s1 to form f1.  f1 is 1/5 of AB. Fold A to s1 to create f3, A to f3 for f4 and f3 to f1 for f2.

With folds horizontal and vertical folds from each of the t1,t2,f1,f2,f3,&f4 we have 15 rectangles of the same size.

Part 2 - displaying n/15's  in part
14/15 - fold A towards o to form the line f3-t2 (area of one 1/15 rectangle removed)
13/15 - fold A towards o to form the line f1-t2 (area of two 1/15 rectangles removed)

Posted by brianjn on 2012-07-25 21:58:43