The five problems of the six domino tiles

Here is a set a problems (regarding domino tiles) of a famous Portuguese newspaper weekly magazine. For each problem you have $$6$$ domino tiles and the goal is always to place them touching each other by the rules of each problem. The touching between two tiles corners is not valid:

You have to display all the six tiles on each problem.

Problem 1:

Display the six tiles so that each one touches only two of the others.

Problem 2:

Display the six tiles so that each one touches only three of the others.

Problem 3:

Display the six tiles so that each one touches only four of the others.

Problem 4:

Display the six tiles so that each one touches all of the others.

Problem 5:

Display the six tiles so that

• one touches only one of the other
• one touches only two of the others
• one touches only three of the others
• one touches only four of the others
• one touches all of the others

Note #1: I decided to put all the problems on the same post mainly because all of them have the same statement, but also because some of them are really easy.

Note #2: You don't really have to use domino tiles. You could picture $$2\times1$$ blocks instead (the values of the domino faces don't matter here). I just used domino tiles to be faithful to the original post.

• In problem 5 you only specify what five of the dominoes do. Is that correct? Jul 29, 2020 at 12:01
• @JaapScherphuis, yes!
– Pspl
Jul 29, 2020 at 12:31

Problem 1:

(there's a hole in the center, it's not a tile)

Problem 2:

on top of

Problem 3:

on top of

Problem 4:

Not exactly to scale, Excel isn't the right tool for these kind of drawings. The blue ones are $$6\sqrt2 \times 3\sqrt2$$ cells wide, but the configuration works if they're $$8 \times 4$$ cells wide as the black ones.

Problem 5:

(same caveat as Problem 4)
The top right tile touches only one other tile
The bottom right tile touches two others
The bottom left tile touches three others (as does the horizontal one)
The bottom center tile touches four others
The blue tile (on top of the others) touches all others

• I’ve never thought of 3D! Jul 29, 2020 at 12:29
• Just the fourth and the fifth to go :)
– Pspl
Jul 29, 2020 at 12:32
• @Pspl I think I've solved them as well. Thanks for sharing the puzzle! Jul 29, 2020 at 12:50
• @Glorfindel, yes! You did solve them all. The only different solution I have from you is regarding the last problem. But yours works as well :)
– Pspl
Jul 29, 2020 at 12:53

Problem 1

The middle is a hole

• Can you figure out different solutions for the others? Relatively to @Glorfindel answer... I know different solutions for all of them, except for the fourth.
– Pspl
Jul 29, 2020 at 12:56
• @Pspl Which problems do not have 2D solutions? Jul 29, 2020 at 13:11
• Only the first one has a 2D solution (as far as I know).
– Pspl
Jul 29, 2020 at 14:00