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Watch the little bee buzz around the flower garden. Pay particular attention to how he picks up or drops off pollen (i.e., a single letter) at each flower.

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Notice:
— The little bee visits each flower exactly once
— The little bee can land on either the right side of the flower word or the left side of the flower word
— As he departs from the flower, the little bee can either leave pollen (i.e., a single letter) on the flower or take pollen (i.e., a single letter) from the flower.
— The flower must always show a valid English word before, during, and after the bee's visit
— The little bee never flies naked. He is always carrying some pollen (letters) with him. (Why? Because otherwise you won't get the triple word effect, with three different words on the flower before, during, and after the bee's visit.)
— The letters that the little bee carries do not need to be a word. He is flying too fast for anyone to read anyway!


Now it's a new season, with a new bloom of flowers. See if you can figure out which letters the little bee initially brings with him into the flower garden, and in which order he must visit the flowers.

puzzle_flower_garden

In case you can't read the flowers:

BROWS

DIVER

EMISSION

EMOTION

ORATION

RAILING

REGAL

REGIME

SHREW

SURGING

TRAIN
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  • $\begingroup$ @Veskah — Yes, you can just give the initial state of the bee and list the flowers he visits in order. No need to draw anything! $\endgroup$ – SlowMagic Sep 3 at 14:11
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    $\begingroup$ I found it interesting that you added the no-computers tag! Even skillful developers would have a hard time with the algorithm for this as there are a lot of possibilities. $\endgroup$ – PerpetualJ Sep 3 at 14:18
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    $\begingroup$ @PerpetualJ — I've been surprised by how fast people can whip up a computer program to solve very intricate puzzles! $\endgroup$ – SlowMagic Sep 3 at 14:30
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    $\begingroup$ Well, I suppose if you have a dictionary handy then it’s more plausible but still, brute forcing this one would take some time lol $\endgroup$ – PerpetualJ Sep 3 at 14:33
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    $\begingroup$ @Supersonic ahh, alas, outside of my realm of expertise! :) Great point though! $\endgroup$ – PerpetualJ Sep 3 at 15:46
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The little bee starts with:

$\text{NTED}$

Path:

\begin{array} {|c|c|}\hline \textbf{Before} & \textbf{Now} & \textbf{After} & \textbf{Remaining} \\ \hline \text{REGIME} & \text{REGIMENTED} & \text{REGIMEN} & \text{TED} \\ \hline \text{DIVER} & \text{DIVERTED} & \text{DIVERT} & \text{ED} \\ \hline \text{REGAL} & \text{REGALED} & \text{REGALE} & \text{D} \\ \hline \text{EMOTION} & \text{DEMOTION} & \text{MOTION} & \text{DE} \\ \hline \text{RAILING} & \text{DERAILING} & \text{AILING} & \text{DER} \\ \hline \text{SHREW} & \text{SHREWDER} & \text{SHREWD} & \text{ER} \\ \hline \text{BROWS} & \text{BROWSER} & \text{BROWSE} & \text{R} \\ \hline \text{EMISSION} & \text{REMISSION} & \text{MISSION} & \text{RE} \\ \hline \text{SURGING} & \text{RESURGING} & \text{URGING} & \text{RES} \\ \hline \text{TRAIN} & \text{RESTRAIN} & \text{RAIN} & \text{REST} \\ \hline \text{ORATION} & \text{RESTORATION} & \text{RATION} & \text{RESTO} \\ \hline \end{array}

Method I used:

The main points to note are that letters $\text{N}$ and $\text{D}$ must be in the set of start letters because else there's no way to make valid words with REGIME and SHREW respectively (I think? Didn't find any possibilities) and it doesn't look possible to extract them from any word.

I don't think there are any words ending in DIVER, and words with it are limited too. Only viable words I can think of were DIVERSE, DIVERT and DIVERTED. I wrote that down to do a casework and went the DIVERTED path because we already have a $\text{D}$ and NTED works with REGIME, which happened to be correct and I didn't have to do a casework :)

Now I started working in reverse. After thinking on ORATION I noticed that RESTORATION is good because it could be obtained by RESTRAIN. The only possible place to get $\text{S}$ is SURGING and it was 3-way compatible too so I moved on to that.

And now we have to get an $\text{E}$ for which we can use both EMISSION and EMOTION, and I chose EMISSION thinking of coming back later if I got stuck, but I think choosing EMOTION would have lead to an answer too (Here just $\text{R}$ is remaining now)

Now I went back to DIVERTED. We can have an ED or RTED remaining, and as it is not possible to put RTED anywhere I chose ED.

Here I got stuck for some time as I didn't know the word REGALE. I was thinking of going back, but fortunately I checked the dictionary for each word adding -ED and found that REGALED exists. :) (Just $\text{D}$ is remaining here)

Now I looked at SHREW. The only way that I could think that could tackle this is going SHREWDER and SHREWD, which leaves us with ER.
The only remaining word which works with ER is BROWS, and making BROWSE leaves us $\text{R}$! Now we have a clear path from SHREW to the end.

Now it was just about how to make DER for SHREW. As we have $\text{D}$ from REGALED and the remaining words are EMOTION and RAILING, both words such that removing the first letter gives a valid word and has first letters ER a path is found!

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    $\begingroup$ Yes, my dictionary agrees with Wiktionary. It is a verb, and it takes on the ending —ING in the present tense. $\endgroup$ – SlowMagic Sep 3 at 16:27
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    $\begingroup$ Thanks for checking! I'll edit that out. :) $\endgroup$ – Supersonic Sep 3 at 16:28
  • $\begingroup$ Excellent work. And thank you for describing your solving method. $\endgroup$ – SlowMagic Sep 4 at 18:26

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