Long -1
The diagram represents a small sheet of 12 postage stamps, as they are usually sold, all perforated at the edges and all of the same value. (The letters are only there to identify the separate stamps).
You need 4 of the stamps in order to post a letter but would like all 4 to be properly joined together at their edges (not at their corners). For example: ABCD, EFGH, JKLM, FGHL would all do, but NOT EFLM.
In how many different ways can you get such a group of 4?
(Only the number of ways is required, not a listing)
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The answer is 65.
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1 solution
Just recall that the shape would be exactly the same as Tetris objects. To count easily, you map the outlining rectangular shape that could be had from the 12 stamps. Like the Is use 4×1 rectangle, so there should be only 3 horizontal mapping allowed. For the 2×2 square, there are 6. For other shapes, they would each need a 3×2 rectangle, and there are 7 ways to map 3×2 out of 4×3. For each L shape, there are 4 permutations inside one 3×2 rectangle. T shape has 2 and Z/N shape allowed another 2. Total = 3×1 + 6×1 + 7(4+2+2) = 65.