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These are pentominoes, with letter codes:

enter image description here

Create 4 yes/no questions which uniquely classify each pentomino.

Examples of such questions are:

  • Does it have rotational symmetry?
  • Does it have reflection symmetry?
  • Is it the net of an open box?
  • Does it have point symmetry?

The idea is to create a set of questions where no pentomino has the same answers as another.

Source: https://www.mathsisfun.com/pentomino_challenge.html

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    $\begingroup$ A bit irritating that they used some non-standard letter designations (M instead of W, N instead of S or Z, and Z instead of N) $\endgroup$ May 6 at 14:38
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Here my first go:

  1. Does it fit (perpendicularly) inside a rectangle smaller than 9 squares of area?
  2. Is there a square with more than 2 neighbours?
  3. Can you rotate the mirror image of the piece back to the original?
  4. Find the longest straight run that isn't a dead end at both ends. Is it exactly three squares long?

enter image description here

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Not sure if this kind of reasoning is allowed, but:

this seems trivial if we can simply refer to the letter labels themselves. e.g. four questions could be:

Q1: Is the letter in TUVXYZ?

Q2: Is the letter in FILTUV?

Q3: Is the letter in LMNUVX?

Q4: Is the letter in MFVY?

Each pentomino will have a unique set of answers to those four questions.

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  • $\begingroup$ There was a comment similar like this, using rows and columns. But it was deleted. $\endgroup$ May 7 at 2:55
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Late answer:

                                       U:      P:      N:
                                       ┌┬┐     ┌┬┐     ┌┐
                                       ├┼┘     ├┼┤     ├┼┐
                                       ├┼┐     ├┼┘     └┼┤
                                       └┴┘     └┘       ├┤
                                                        └┘

square bbox: False False False cut from ∞ "+": False False False simultaneously sort x and y: False False True connect □ centres w/o leaving: False True False

Y: L: I: ┌┐ ┌┬┐ ┌┐ ├┼┐ ├┼┘ ├┤ ├┼┘ ├┤ ├┤ ├┤ ├┤ ├┤ └┘ └┘ ├┤ └┘ square bbox: False False False cut from ∞ "+": True True True simultaneously sort x and y: False True True connect □ centres w/o leaving: False False True

F: Z: W: ┌┬┐ ┌┬┐ ┌┬┐ └┼┼┐ └┼┤ └┼┼┐ ├┼┘ ├┼┐ └┼┤ └┘ └┴┘ └┘

square bbox: True True True cut from ∞ "+": False False False simultaneously sort x and y: False True True connect □ centres w/o leaving: False False True

T: X: V: ┌┬┬┐ ┌┐ ┌┬┬┐ └┼┼┘ ┌┼┼┐ ├┼┴┘ ├┤ └┼┼┘ ├┤ └┘ └┘ └┘

square bbox: True True True cut from ∞ "+": True True True simultaneously sort x and y: False False True connect □ centres w/o leaving: False True False

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