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Suggestion:  A [QUIZ] in the subject of emails about the problem helps everyone
on Ruby Talk follow the discussion.

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by Matthew Moss

You have a square sheet of grid paper, 16 cells across by 16 down. A number is
written in each cell, starting at 1 in the upper-left corner, going across each
line then down the paper, ending with 256 in the lower-right corner.

Your task is write a Ruby function to fold the paper in half repeatedly (along
the horizontal or vertical middle), until you are left with a single cell, 256
layers thick, and report back on the order of those layers, top to bottom.

The input to the function is a string containing the characters "T" (the top
edge folded down to the bottom edge), "B" (bottom up to top), "R" (right to
left) and "L" (left to right). Not every combination of those will be valid, so
make sure you verify your input.  Output will be an Array of Integers from 1 to
256, arranged in the top-to-bottom layer order after all folds are done.

To help clarify, here's a 2x2 example.

+-+-+
|1|2|
+-+-+
|3|4|
+-+-+

fold("RB") => [3, 4, 2, 1]
fold("TL") => [3, 1, 2, 4]
fold("LR") => raise exception for invalid input

the dimensions of the paper; dimensions should be power-of-2 in order to fold
down to one cell.

Extra extra credit:  Write a method check_fold() that takes the resulting Array
of Integers from the quiz and returns the transformation String argument (i.e.
fold(check_fold(final_order)) == final_order).

```