Puzzling Asked on October 22, 2020
Starting with 27 small cubes connected to each other in a 3x3x3 cube shape, I removed some of the cubes so that all the remaining cubes stayed solidly connected by cube faces.
I then used the resulting object as a stamp: I touched one face in ink and pressed it on paper. After doing this for 3 faces of the object, I had managed to spell out the word TOY:
X X X X X X X X X X X X X X X X X
Question 1. (the original question): Which letter can be stamped using the face that’s opposite to the O face?
Question 2. The face opposite the T face can also be used to stamp a clearly recognisable letter. Which one?
(nb. The question didn’t originally specify that the small cubes had to fit inside a 3x3x3 volume and be connected by cube faces.)
Answer to the original question "What pattern can you print with the face opposite the O?":
You can make
That would be because in a 3x3x3 cube
Since the face with the Y has no such edges,
Answer to the question that OP edited in later:
Making the bold assumption that the side opposite the T also prints a clearly recognisable letter, it's going to be
That would be because the side opposite the T must be one of these two:
There are no other possibilities, because there's only one way the T side can connect to the O and Y sides, and the corner pieces on the Y side need to be connected face-wise to the rest of the shape. (They aren't connected on the Y side.)
To see this clearly, here's a 3D model of the three known sides:
Correct answer by Bass on October 22, 2020
As far as 3x3 gridded shapes go:
Answered by Paul Panzer on October 22, 2020
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