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


**How can a honeybee visit all cells
exactly once in this crescent shaped honeycomb,
beginning at the bottom tip and ending at the top?**

- The starting cell, at lower left, has 1 drop of honey.
  All other cells begin empty.

- Each step consists of moving to an adjacent cell and
  filling it with **0**, **1** or **2** honeydrops,
  based on how many total drops
  its (1 to 6) neighboring cells, combined, contain **at that moment**.

- The number of new honeydrops is the remainder of the surrounding total
  when divided by 3.

$$\small \begin{matrix}
\textsf{Total adjacent drops} ~&~ 0,3,6,9,12 ~&~ 1,4,7,10 ~&~ 2,5,8,11 \\
\textsf{Number of new drops}  ~&~ 0          ~&~ 1        ~&~ 2         \\
\end{matrix}$$

- The top cell, marked `(1)`, is empty at first
  but should receive 1 honeydrop when it is reached.

- The six cells with **0** should receive 0 drops when they are reached.
  (The sums of their neighbors&rsquo; drops
   should be multiples of 3 at those moments.)
  Other cells may also receive 0 drops.

The following sequence of eight steps demonstrates
how the bottommost **0** cell might be reached.

&emsp;
<img src="https://i.sstatic.net/AdWvp.png">

In this example, division by 3 comes into play when
the last cell to receive **1** drop, on the seventh step,
has a total of 1+2+2+2&thinsp;=&thinsp;7 drops in its adjacent cells,
giving a remainder of **1** when divided by 3.
The eight step correctly reaches the **0** cell
as 1+2&thinsp;=&thinsp;3, which leaves **0** remainder when divided by 3.


This puzzle forthrightly, though incompletely, imitates
[_Two honeycomb hints_](http://puzzling.stackexchange.com/questions/42884)
by
[Yuriy S](http://puzzling.stackexchange.com/users/30250/yuriy-s).

This is meant to be convenient on paper and in a text editor.
&hairsp;
Here is a template for `<pre>...</pre>`:
<pre>
                                                         ___
                                                        /(1)\___
                                                        \___/   \
                                                            \___/
                                                            /   \___
                                                            \___/   \
                                                            /   \___/
                                                            \___/   \___
                                                            /   \___/ 0 \
                                                            \___/   \___/
                                                         ___/   \___/   \
                                                        / 0 \___/   \___/
                                                        \___/   \___/   \
                                                     ___/   \___/   \___/
                                                    /   \___/   \___/ 0 \
                                                    \___/   \___/   \___/
                                                 ___/   \___/   \___/
                                                / 0 \___/   \___/   \
                                                \___/   \___/   \___/
                                             ___/   \___/   \___/
                                         ___/   \___/   \___/ 0 \
                             ___     ___/   \___/   \___/   \___/
                            / 1 \___/   \___/   \___/   \___/
                            \___/   \___/   \___/ 0 \___/
                                \___/   \___/   \___/
</pre>