A letter by Serhiy Grabarchuk on Paper folding problems

Some interesting info on Stamp Foldings can be found at:
http://www.theory.csc.uvic.ca/~cos/inf/perm/StampFolding.html .

We have at Puzzles.com a growing collection of different
folding puzzles; see our PuzzlePLAYGROUNG sector:
http://www.puzzles.com/PuzzlePlayground/Folding.htm .

Also we have one puzzle - The Origami Checkerboard Puzzle - at:
http://www.puzzles.com/PuzzleClub/CheckeredOrigami/CheckeredOrigami.html .

There are two sites with many additional challenges to
this puzzle. These are Origami Checkerboard Puzzles at
the OrigamiUSA site:
http://www.origami-usa.org/puzzles%202.htm , and

Sasaki's Puzzles at the British Origami Society site:
http://www.worthhall.demon.co.uk/fun/sasaki.htm .

At the OrigamiUSA you can also see another type of Origami
puzzles - Origami Area Puzzles:
http://www.origami-usa.org/puzzles%201.htm .

In November of 2000 Ed Pegg Jr. published at his site
www.mathpuzzle.com Junk's Origamic puzzle (or Junk Kato's
Triangle); now you can find a few solutions to it and some
further links on the theme at:
http://www.mathpuzzle.com/katotriangle.htm .

There are different well-known Flexagons described in Martin
Gardner's columns and books. See for example:
http://home.xnet.com/~aak/hexahexa.html .

Also add to the list one of the best folding puzzles ever - Arthur
Stone's Flexatube:
http://mathworld.wolfram.com/Flexatube.html .

A clever Origami puzzle seen from one more point of view is
proposed at:
http://home.istar.ca/~wko/origami_puzzle.html .

A clever combination of the Tangram pattern and Origami -
Tangram Folding - is shown at:
http://www.thok.dk/tangram.html . It's more like a piece of art,
though.

At Sy Chen's Paper Folding Page
( http://users.erols.com/sychen1/pprfld.html ) you can see
a well-known philisophycal and puzzling symbol folded of
a single Origami b/w sheet:
http://users.erols.com/sychen1/Photos/jpg/TaiChi.jpg .

There you can see also Tangram Square folded using just a square
of paper:
http://users.erols.com/sychen1/Photos/jpg/TangramSquare.jpg .

Many different folding puzzles you can find in Martin Gardner's
books. For example see Wheels, Life, and other Mathematical
Amusements, Chapter 7, The Combinatorics of Paper Folding,
pp. 60-73. It contains a lot of folding puzzles and a further
bibliography.

Also there is a small but fascinating book Paperfolding Puzzles