

An Origami triangle.


How to get a 2unitside checkered
triangle.


Three 2unitside checkered
triangles.


Fiftynine 3unitside checkered
triangles.




This is a triangular version of the Origami Checkerboard
puzzle. It is also a rare triangular Origami work since
it uses a sheet of paper in the form of an equilateral
triangle colored just on one of its sides.
A small sample at left shows how to get a 2unitside
triangle with one colored cell.
In this page you can see three, 2unitside patterns,
and fiftynine 3unitside patterns. Your challenge is
to achieve every of the proposed patterns in the minimum
of single "book" folds. The final shape every time is a
flat equilateral triangle; no matter what pattern will
be at its back. Numbers next to the patterns indicate
the minimal known numbers of folds necessary to perform
them.
Write us if you can improve any of these results.
Pattern 6U, solution to it, and solutions to patterns
3c, 4I, 5W, 5X, 5Y, 5Z, 5AB, 5AC, 6L, 6M, 6N,
6O, 6Q, 6R, 6S, and 6T were found by Keiichiro
Ishino. A solution to pattern 5AA was found
independently by Setsuo Sasaki and Keiichiro Ishino.
Solutions to patterns 3b and 3J were found by Hirokazu
Iwasawa and Naoaki Takashima, respectively.
***
Much more difficult challenges can be finding all the
4unitside checkered triangles and, then, finding their
minimal solutions. Recently, Keiichiro Ishino calculated
that there are 6,605 substantially different 4unitside
checkered triangles. Part of them have their solutions
quite similar to the respective 3unitside checkered
triangles described here, but it is obvious that most of
them are rather difficult to be optimized. 


