The T(ea)-puzzle: Tangram reinvented

IMG_0002Four cardboard pieces were included in a box of White Rose Ceylon Tea distributed by Seeman Brothers of New York in 1903. On one of the pieces was written: “Arrange these four pieces of cardboard so as to form a perfect T. White Rose Ceylon is a perfect Tea.” This puzzle has been copied many times, mostly simply known as T-puzzle. When you see the solution (shown here to the right), then this puzzle seems obviously simple. However, when you are given the pieces disassembled, then the assembly appears to be really hard.

In a way, the pieces are reminiscent of Tangram (see my earlier post), so one might ask whether there are other figures that can be made with the pieces of the T-puzzle. Ever since Martin Gardner’s book Wheels, Life and other Mathematical Amusements (1983:132) two other nice figures were known that could be made with these same pieces. But now the iPhone game Songram (and Songram Lite) present dozens of new figures to be made! Due to the strange form of the one piece, even a simple long rectangle (see left) becomes tricky.

IMG_0001All these new forms to be made really seem to be a new invention of the current developers, though they claim in their description of the puzzle that “thousands of Chinese people over last hundreds of years have played Songram”. That really doesn’t make sense. As I summarized previously in my post about Tangram, the Tangram puzzles arose around 1800, and the name “Tangram” was made up in the US in 1848. A name like “Songram” is surely not Chinese, and the puzzle cannot be really old. This is just marketing fancy!

There is another version of the same game available in the app store: iTangram. It looks like a ripoff Songram, but maybe both are a ripoff of yet another puzzle?

Finally, just a little note on the form of the pieces in comparison to Tangram. The Tangram pieces can be analyzed as being constructed from triangles: two small triangles, three pieces with double the surface area of those triangles (formed by combining two small triangles), and two large triangles with four times the surface area of the small triangles.

The T-puzzle pieces can be analyzed as consisting of a triangle (with sides 1, 1 and √2) and and a rectangle (with sides 1 and √2-1). The four pieces of the puzzle can then be constructed as follows:

  • 1 triangle
  • 1 triangle + 1 rectangle
  • 3 triangles + 1 rectangle
  • 3 triangles + 2 rectangles

Holding this composition in mind makes solving the puzzles much easier!

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