Allan's Trominoes Puzzle
Here are the only two possible trominoes:
Can you fill the grey shape (that looks like a Corona virus) with the above trominoes (no "holes", no overlappings)?
The solution seems to be unique (and was designed to embed a 6 x 6 compact "block" delimited by the blue square):
Is this the unique tiling of the above grey shape with trominoes?
Allan W. had asked on Math Fun yesterday how large could be such a "blue block" when tiled in an unique way by trominoes. You might try to build a 6 x 7 or a 7 x 7 (or a larger!) such block.
For 1, 2, 7, 8, a, b, d, g, f, j, k, L it is physically impossible to make a different choice for the given shape. Then you see that from the upmost 3 you cannot go straight down because it would isolate the square of the leftmost "e", so an L-shaped 3 is the only choice here. Similar for 4, 5 and 6: It is immediately obvious that there is no other possible choice for these. Then, c, e, h and i are forced, too. It would be more interesting to know whether there are forms which cant' be solved straightforwardly, e.g. which would require "backtracking" or some more advanced reasoning.
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