# Middle out: A puzzle that won't behave

### Ah, jeez. You'd think making puzzles was easy.

What kind of fool thinks he can turn up and instantly turn in a working puzzle on his first try? I've been checking my pocket calculator and rolling die after die but with all my luck I still can't figure this one out.

I got my hopes up when the middle one was easy, but that's the only one that just tells you what it is. The corners still seem to be undergoing some kind of nondeterminism. Darn it, I thought the underlying rules were fully specified!

It seems the puzzle is deeper than it looks, and I still haven't completed it.

Unless... perhaps Puzzling wants to help me finish it? I just need to find out what that "?" block should be, though I keep finding contradictory answers...

• Well, I could make out fancily written letters in the order : 'b', 'E', 'A', 'E', 'S', 'Y', 'G', 'o', 'd'. Probably with these one may guess what is being required (like 'EASY' is shown clearly and remaining letters should form meaninigful words like 'BE', 'GOD' ... or some anagrams of these). Sep 22, 2017 at 15:43
• When the gif ends, it crashes the webpage for me on an iPhone 4S. Does it loop infinitely? Sep 22, 2017 at 20:01
• @boboquack Yes, it's an infinite loop. Sep 22, 2017 at 20:09
• Here's a revamp of the puzzle. Hopefully it's more manageable like this. Sep 23, 2017 at 2:43
• @Veedrac Looking at Alconja's answer, I think I've got the idea. At least, I think I can see how they all work except for the 9... could you just make sure the 9 is correct? Sep 23, 2017 at 3:49

## 1 Answer

The bottom figure has two states of non-determinism (assuming the pattern is restricted to the given ten spaces, otherwise there are arguably three states). Specifically, the bottom shape will look like this:

Because each figure is:

effectively a single digit (0-9), displayed as it would be on a seven segment display, except then projected onto the edges of a cube. The trick is that the digits are projected onto their cube whilst in the centre spot of the grid and then the cube is rotated/rolled to its correct position (based on a standard calculator layout). Cubes are rolled when moving vertically and rotating when moving horizontally (clockwise when moving left, anticlockwise when moving right). The non-determinism comes from whether you roll then rotate, or rotate then roll.

So, the missing digit is the zero, which can reach it's position from the centre via either of the following paths (with semitransparent cubes, to make it clearer what's going on):

• @Wen1now Yes, I already mentioned that one. Your flipped 7 the same as my vertically flipped L. I'll write it up more clearly when I'm not on mobile. Sep 23, 2017 at 3:59
• Oh. Then I think you're missing the L flipped horizontally (roll,roll,rotate) Sep 23, 2017 at 4:01
• @Wen1now yeah, I explicitly left that out under the assumption that the movement needed to stay within the existing positions (note my two vs three states comment) Sep 23, 2017 at 4:02
• @Wen1now except I've just noticed my stupid mobile autocorrect made it "the states" instead of "three states", which is probably why it's confusing... Sep 23, 2017 at 4:04
• Nice work on the pictures! Oct 13, 2017 at 10:29