Pentomino Challenge
These are pentominoes, with their letter codes:
The challenge is:
Create four yes/no questions that 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.
The challenge is harder than it looks.
Example
Rotational Symmetry 
Reflection Symmetry 
Open Box  Point Symmetry 

F  no  no  yes  no 
I  yes  yes  no  yes 
L  no  no  no  no 
M  no  yes  yes  no 
N  yes  no  yes  yes 
P  no  no  no  no 
T  no  yes  yes  no 
U  
V  
X  
Y  
Z 
... so these four questions do not work ... the answers for T are the same as for M ... !
Can YOU think of four questions which will work?
(You can discuss this at the forum.)
This is based upon an investigation by L Mottershead. Sources of Mathematical Discovery