**Wrap-up: the making of
[_Honeydripping
 around the clock_](http://puzzling.stackexchange.com/questions/44090/)**

_This is not a solution to the puzzle but provides notes from its poser.
 This type of answer has been
 [approved by the community](https://puzzling.meta.stackexchange.com/questions/5420/)._

_**Caution:** This post contains information about the solution._

- - - - -

This is the third experiment with self-defining
[hexagonal-tiling](https://en.wikipedia.org/wiki/Hexagonal_tiling)
mazes inspired by
[_Two honeycomb hints_](http://puzzling.stackexchange.com/questions/42884/)
and, especially,
[_Two honeycomb hints, part two_](http://puzzling.stackexchange.com/questions/42887/)
by
[Yuriy S](http://puzzling.stackexchange.com/users/30250/yuriy-s).

[<img src="https://i.sstatic.net/GtLDq.png" height="80">](http://puzzling.stackexchange.com/questions/42884/two-honeycomb-hints-yet-another-find-the-next-number-in-the-sequence)
&emsp;&emsp;&emsp;&emsp;
[<img src="https://i.sstatic.net/IYEjO.png" height="80">](http://puzzling.stackexchange.com/questions/42887/two-honeycomb-hints-part-two-find-the-next-number)

The first experiment was a simple compact maze
with unwieldy sums:
[H-one-one-oneycomb](http://puzzling.stackexchange.com/questions/43800/).
Next came a maze with almost-trivial sums
and additional guiding features:
[How to fill a honeymoon](http://puzzling.stackexchange.com/questions/43936/).

&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;
[<img src="https://i.sstatic.net/eb1GG.png" height="70">](http://puzzling.stackexchange.com/questions/43800/h-one-one-oneycomb)
&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;
[<img src="https://i.sstatic.net/UZpFw.png" height="140">](http://puzzling.stackexchange.com/questions/43936/how-to-fill-a-honeymoon)

So it was time to explore structures
whose traversals could feel more like journeying
than like space-filling.
The conceptual point of departure was to simply have a
hexagon made of hexagons made of hexagons,
which led to a variety of possible forms.

<img src="https://i.sstatic.net/J1Tys.png">

The purest version of the hexagonal concept,
marked **12** here,
turned out to be too repetitive to be interesting.
Version **7** felt like a discovery more than a construction,
with it&rsquo;s beautifully paradoxical harmonization of
6-fold and 7-fold symmetries,
as it naturally includes many different local configurations.
Version **10** wound up with rounded corners,
to avoid unnecessarily many small-scale decisions,
and that suggested the final clock format.

Would have been descriptively clean to
begin the maze at **1** o&rsquo;clock and end at **12**,
but that allowed two very different overall routes,
one that was an all-too-regular zig-zag
and another much more interesting route that included
a sneaky counterclockwise inner loop
along with some zig-zags.
Both routes had the lucky feature of
forcing the hours to be visited in order.
Hah, beginning at **12** would
allow only the more interesting route.

>! <img src="https://i.sstatic.net/fw2kH.png">

Now to check if this is plain too easy to
solve&hairsp;&mdash;&hairsp;or,
more likely, too tedious,
especially as arithmetic mistakes could require redoing a lot of work.
A few sloppy failed test solutions were enough to realize
that it wasn't too easy and that, surprise,
most arithmetic mistakes had only local effects.
Some analysis revealed three particularly forgiving lucky features,
labeled **A**, **B** and **C**.

>! <img src="https://i.sstatic.net/PfVW8.png">

**A** demonstrates that **2**, **3** and **4** o'clock
add a combined 0 to the running total.
**B**&nbsp;demonstrates that any sum (or mistake)
arriving at **2** or **8** o'clock
will be multiplied by 5, which turns
all even sums$\scriptsize\raise.2ex/$mistakes into 0
and prepares odd sums$\scriptsize\raise.2ex/$mistakes
to become 0 at their inevitable next doubling.
**C**&nbsp;demonstrates that the clock&rsquo;s inner loop has no net effect
on the peripheral loop at **9** o'clock&mdash;whew!

More fun than anticipated to analyze and test solve,
for hours and hours,
this was ready to be posed.