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What is an opposite face to the letter $T$?

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:

enter image description here

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.)

2 Answers

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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