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On the left is a L pentomino. On the right is an T tetromino.

There is a particular shape (holes are permitted) that you can build with four copies of the piece on the left, or with 5 copies of the piece on the right. You may rotate and flip the pieces, but they cannot overlap. What shape can you build?

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!

EDIT: 48 hours have now passed. Everyone may post answers now.

This puzzle is from: http://skepticsplay.blogspot.com/2010/04/polyomino-equations.html

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    $\begingroup$ I have found an answer, and I'd like to say its quite elegant. Will refrain from posting though. $\endgroup$
    – Stevo
    Commented Nov 8, 2023 at 6:53
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    $\begingroup$ Did you know there are actually two solutions ? (not counting reflections/rotations obviously) $\endgroup$
    – Jaap Scherphuis
    Commented Nov 8, 2023 at 9:57

2 Answers 2

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As the 48 hour mark has gone by, I will post one of the solution(s) I found while merely just playing with the pieces:

enter image description here

and subsequently

enter image description here

This was mainly made with the understanding that there probably would have been a hole in the middle of the shape itself, and understanding the shape when 2 T shapes makes one side a tile longer came in itself to the solution.

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For completeness, here is the second solution. I have used the images from Stevo's solution, and flipped over the bottom-right section.

enter image description here

enter image description here

I used a computer to find all solutions that fit within a 6x8 rectangle, and they were all equivalent to one of these two solutions.

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  • $\begingroup$ Bonus challenge: do solutions exist for any 5 x tetromino paired with a 4 x pentomino? Probably too hard for a puzzle :) $\endgroup$
    – Dmitry Kamenetsky
    Commented Nov 10, 2023 at 13:10
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    $\begingroup$ @DmitryKamenetsky Solutions are known for all but two combinations. That site is rather old so maybe the two missing ones have been found by now. $\endgroup$
    – Jaap Scherphuis
    Commented Nov 10, 2023 at 13:12
  • $\begingroup$ Oh very cool! Some solutions are large! $\endgroup$
    – Dmitry Kamenetsky
    Commented Nov 10, 2023 at 13:28
  • $\begingroup$ ah this is the polyomino compatibility problem $\endgroup$
    – Dmitry Kamenetsky
    Commented Nov 10, 2023 at 13:29
  • $\begingroup$ even 3 tiles are possible: sicherman.net/rosp/triplep.html $\endgroup$
    – Dmitry Kamenetsky
    Commented Nov 10, 2023 at 13:32

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