# Test of Pentominoes

These are pentominoes, with letter codes:

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.

• 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) May 6, 2021 at 14:38

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?

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.

• There was a comment similar like this, using rows and columns. But it was deleted. May 7, 2021 at 2:55

                                       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