13

I think the answer is using the following coloring: For other board sizes, Reasoning:


11

I think the answer is this Explaining $16$ possible solutions Some notes on how the solution is obtained.


9

Since a single line doesn't do damage, it is possible to do To achieve this, there are a couple of requirements: To get these pieces one after the other For this to occur so that the final piece also clears the board, we get these constraints on the number of pieces $X$: Given these, the smallest $X$ that satisfies both requirements is This is a small ...


8

If I understand the game correctly,


7

I guess, I'm too late, but I propose


7

Unless I made a mistake somewhere, this solution is unique: To get there, I used a couple of rules of thumb: Apart from those, there were a couple of slightly mind-boggly deductions required, but all in all, everything seemed extremely well designed, and no guesswork was needed at any point. Progress, part 1: Progress, part 2: Progress, part 3: ...


5

This has been hard work... may I not explain my approach?


4

Logical deduction:


3

As an upperbound, I can attack as little as with by following configurations:


3

@Daniel_Mathias gave a very helpful link which has all the 12x5 solutions in a text file. So some simple code allows us to see that of the 1010 12x5 solutions, there are 264 with 1 straight cut. But, sadly, none with 2 or more cuts. A few examples of the former are: 12 FFPPP IIIIINN LFFPP ZZWNNNT LFXUU VZWWTTT LXXXU VZZWWYT LLXUU VVVYYYY 81 ...


3

There are no solutions in three rectangles. For an index of all pentomino solutions: Pentominos home Index of 5x12 solutions A particular solution you may be interested in: #747


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