by Smythe Dakota » Tue Nov 27, 2012 10:31 am
In each cell, each of the 7 LED segments can be in any of 4 states, so for each cell there are 4^7 possibilities, i.e. 16384 different possible values.
Actually, there is also a 16385th possibility, namely, that the cell is completely blank. (This alternative could, however, simply be an abbreviation for "all LED segments are grey" or something.)
So it seems highly likely this could be some kind of N-puzzles-in-one thing, where N is perhaps 3 or 4.
For example, with N=3, the upper left and upper right LED segments could be assigned a value as follows:
red-red = blank
red-green = 1
red-blue =2
red-grey = 3
green-red = 4
green-green = 5
green-blue = 6
green-grey = 7
blue-red = 8
blue-green = 9
-- and we could continue this pattern up to 15, if we needed to, but 1-9 (plus blank) is enough for ordinary sudoku, thank you.
Similarly, we could pair the lower left and lower right, which would generate a second puzzle completely unrelated to the first.
And the top and bottom could be paired, generating yet a third puzzle.
The middle segment could just be there for decoration.
For that matter, we could make N=4 (instead of N=3) by using base-10 instead of base-16. For example, the four possibilities for each LED segment could be assigned values as follows:
upper left = 0,1,2,3
upper right = 0,4,8,12
lower left = 0,16,32,48
lower right = 0,64,128,192
top = 0,256,512,768
bottom = 0,1024,2048,3072
middle = 0,4096,8192,12288
By adding these values together, we can generate any number from 0 through 16383 for each cell.
The rightmost digits in the resulting numbers in each cell would then constitute Puzzle A, the next (tens) digits Puzzle B, the third (hundreds) Puzzle C, and the fourth (thousands) Puzzle D.
My only other observation is that, since all the completely blank cells in the original puzzle are on two intersecting diagonals (one NE-SW, the other NW-SE), that Tarek probably has something to do with this, with his wrap-around toroidal and projectively planar ideas.
Bill Smythe