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For this paper-folding puzzle, start with a rectangular sheet of paper. I'm using construction
paper, but thin paper is easier to work with. It should be about twice as wide as it is
high, but the exact dimensions don't really matter. Now carefully fold the paper into
eight panels. Crease all the folds in both directions so that you can easily fold the
entire sheet up into just one panel in a variety of ways.
Now number the panels. On one row write 1,8,7,4. Flip the paper and write 5,6,3,2 across the
other row. I'm also labeling the back of the panels, but that's not necessary.
I read about this puzzle in one of the many collections of Martin Gardner's Mathematical
Games columns. If you like it, check out more of Martin Gardner's books.
To solve the puzzle, fold up the sheet into a single panel so that the panels are all
in order from 1 to 8, with the 1 on top and the 8 on the bottom. When you're solving this
puzzle, you might have to stretch the definition of folding. As long as you can manipulate
the paper into the right configuration without ripping it, don't worry about whether what
you're doing is technically folding.
When you've solved it, you should be able to check your solution by flipping through
the open edge. That's hard to show on video, though, so I'll cut off the edges to prove
that it's solved.
If you solve that puzzle and want a harder one, take a new sheet and label the panels
1,8,2,7 and 6,3,5,4. Again, I would hesitate to call the solution to this puzzle "folding".
But you'll know you've solved it when the panels are in order from 1 to 8. Good luck!