Is it possible to divide the equilateral triangle into 4 pieces and assemble a square with these four pieces, provided that one or two pieces are flipped over to the other side? In other words, I want a mirror reflection of one or two pieces. If this riddle has no solution, I would like to find proof.
Let me remind original solution:
Mind that the blue and green elements in the picture above do not have the same shape. So it is not possible to flip them both to the other side:
Dudeney’s solutions to haberdasher's problem exact measures of sections
Original riddle of Henry Dudeney:
https://www.gutenberg.org/files/27635/27635-h/27635-h.htm#p26
Here is a solution for 5 elements, which of course does not satisfy me.
https://puzzling.stackexchange.com/q/79981/53127
Reason why I seek this solution
The two pictures below may give you a context as to why I posted this question. I am a carpenter, I design and create dinosaur wooden puzzles. This one is based on Henry Dudney's dissection pattern. Assembling the triangle is already deity level difficulty. Unless familiar with Dudney's dissection, the wood grains lead you astray to square. However, the necessity of flipping any piece to the other side is what makes puzzles difficult even for a deity. Here is a video showing an example of dinosaur flip. Even my friends who know that I use a flip to obscure the puzzle, they cannot see that two shapes are complementary, if one is flipped. That is my life goal. Design a puzzle that nobody can solve :-)
