Puzzle Time - Marks on the Die

[jon-nyc]

I have an unlabeled, six-sided die. I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

How many unique ways are there for me to mark the die? (Note: If two ways can be rotated so that they appear the same, then they are considered to be the same marking.)

Extra credit: Suppose you can also mark a face along one of its two diagonals. Now how many unique ways are there to mark the die?

[Klaus]

@jon-nyc said in Puzzle Time - Marks on the Die:

I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

I don't quite understand. What is a mark? A dot? What does "parallel" mean when we are not talking about lines or planes?

[taiwan_girl]

@Klaus said in Puzzle Time - Marks on the Die:

@jon-nyc said in Puzzle Time - Marks on the Die:

I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

I don't quite understand. What is a mark? A dot? What does "parallel" mean when we are not talking about lines or planes?

My question also. How can a dot be parallel to something?

[jon-nyc]

Questionology 101 tells me this is a problem about symmetry and rotation.

So clearly imagine a mark that is not a dot, rather a short line segment in the center of the die face, and drawn parallel to one side or another.

Clearly we would assume that all marks made are identical in length and placement on the face relative to the center, so that we wouldn’t distinguish one set of markings vs another on such factors.

[Klaus]

So you are saying there are only two possible marks for each face? So the answer is 2^6 minus the ones that are the same by rotation?

[jon-nyc]

That’s my read. Otherwise the question becomes “how many distinct marks can you draw” or “how many distinct spots on a face can you put a mark” which seems unlikely for a puzzle.

[Axtremus]

@Klaus said in Puzzle Time - Marks on the Die:

… the ones that are the same by rotation?

Figuring out “the ones that are the same by rotation” is challenging. :man-shrugging: