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enter image description here

Your task is to convert a diamond shape monomino that is made from aluminum foil into an x-shape pentomino (see figures). You may fold the monomino and make one straight cut with a pair of scissors. After the cut, you will unfold the foil and align the separate pieces. The alignment should produce the X-shape shown above, using all pieces of the original monomino. How can this be done without any additional tools?

Note: No overlapping and pieces can be flipped but not need to be attached or joined.

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  • $\begingroup$ Should the cut-off pieces or the remaining foil be an X after the cut? $\endgroup$ – bobble Oct 30 '20 at 17:43
  • $\begingroup$ @bobble -All the foil pieces including remaining piece or pieces $\endgroup$ – TSLF Oct 30 '20 at 17:52
  • $\begingroup$ How? Are the pieces placed next to each other? On top of each other? How are they attached? (This should all be added to the question as clarifications) $\endgroup$ – bobble Oct 30 '20 at 17:55
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    $\begingroup$ This earlier question brings you more than halfway to the answer, as it shows the dissection you are aiming for. $\endgroup$ – Jaap Scherphuis Oct 30 '20 at 19:59
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A solution, and on request an asymmetric solution:

Symmetric:
Cut A=B=C=D to X after folding the blue dotted line in picture 2.
Pieces 1 to 4 are now cut off, and can be moved to make the cross.
note: The initial folds are the 1/4 - 3/4 lines
Asymmetric:
Fold A to X3, D to X1, B to X4
('line' to cut is now X1,X2,X3)
Fold X1X2 to X3X4 and then p to q
cut X4 to X3 [enter image description here

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  • $\begingroup$ Nice.can you do without similar pieces? $\endgroup$ – TSLF Oct 31 '20 at 3:19

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