Inspired by The five problems of the six domino tiles, where one of the tasks was to place six domino tiles so that each tile touches three others (corner / edge touches don't count). My solution there required putting domino tiles on top of each other, and the OP (not the author of the puzzle) thought there is no 2D solution.
Now, if we increase the number of tiles, we can certainly make a 2D solution, e.g. the following one using 16 tiles:
A natural question/puzzle is therefore to ask:
What pattern uses the minimum number of tiles?
- The tiles are twice as long as wide
- Tiles have to be laid out in a two-dimensional pattern
- Each tile needs to touch exactly three others; only touches between edges count
- Just to be pedantic: there needs to be at least one tile