Chrysanthemum bejeweled with dew drops

Question

If you squint, you might be able to see letters in the reflections of some of the dew drops. Those will help get you started.

In this puzzle, the adventure begins just after 12 o'clock and the direction of movement is always clockwise, but the words alternate between reading inward and reading outward.

Starting at the tip of the petal just after 12 o'clock, you should see the word PRICETAG heading inward and doing a dogleg bend down the crease at 1 o'clock.

Then, proceeding from there and read outward to the tip of the next petal (always tending in a clockwise direction around the flower) you should see the word GATEKEEPER.

Notice that you're always using the last few letters of the previous word (but in reverse) to form the first few letters of the next word.

The next word reads inward again, beginning with the four letters R-E-P-E and then four more letters down the 2 o'clock crease. You must complete the word by filling in those last four letters. So, you're looking for a word that looks like REPE _ _ _ _.

Keep going around this way, filling in 17 more words. The 17th word looks like _ _ _ _ _ _ _ ATOR.

The final two words, ROTAVIRUS and SURINAMESE are already filled in.

BTW, don't worry if the words ROTAVIRUS and SURINAMESE seem unfamiliar. All the words that you must fill in are much more well-known.

Answer 1

Solution (Without computer search):

pric//etag
gate/ke/eper
repe/ater
reta/iler
reli/eved
deve/l/oper
repo/rter
retr/i/ever
reve/aler
rela/psed
desp/o/iled
deli/v/erer
rere/le/ased
desa/lin/ated
deta/ined
deni/gr/ated
deta/iled
deli/g/hted
deth/r/oned
deno/min/ator
rota/v/irus
suri/na/mese

Answer 2

Computer-assisted solution

Here's my simple-minded Python code:

words = set(w.strip() for w in open('...')) # dictionary filename here
b1 = [['pricetag','gatekeeper']]
lengths = [8, 8, 8, 9, 8, 9, 8, 8, 9, 9, 10, 11, 8, 10, 8, 9, 9, 11]
def flat1(lists):
    result = []
    for l in lists: result.extend(l)
    return result
for l in lengths:
    candidates = flat1((prev+[w] for w in words if len(w)==l and w[:4] == prev[-1][:-5:-1]) for prev in candidates)
    print(f'after length {l}, #candidates={len(candidates)}')
candidates = [c for c in candidates if c[-1].endswith('ator')]

It would be more efficient to work inward from both ends and then intersect in the middle, and/or to turn the list of words into a map from first 4 letters + length to corresponding words -- but computer time is cheap and simple code has fewer bugs.

(I have in fact implemented the second of those. It does make things way faster.)

I have three word-lists readily to hand on my computer, of different sizes. With the smaller two, or indeed with the union of the smaller two, no solutions were found. I assume they're missing some "ordinary" words. With the biggest, after maybe 10 minutes of grinding (I didn't actually time it so that might be way off) it finds 216 solutions. The one with the simplest words (measured by, first of all, how many are in my smallest wordlist, then by how many are in the second one) still has quite a number of obscurities in it:

pric//etag
gate/ke/eper
repe/ated
deta/iler
reli/eved
deve/l/oper
repo/rter
retr/i/ever
reve/rter
retr/aced
deca/l/iter
reti/c/uled
delu/st/ered
dere/gul/ated
deta/iled
deli/ne/ated
deta/iled
deli/g/hted
deth/r/oned
deno/min/ator
rota/v/irus
suri/na/mese

This one scores a little worse by my metric but seems maybe less obscure; only one word in it gives me pause:

pric//etag
gate/ke/eper
repe//ated
deta//iler
reli//eved
deve/l/oper
repo/rter
retr/e/ated
deta//iler
reli//eved
deve/l/oped
depo/s/itum
muti/ne/ered
dere/gul/ated
deta//iled
deli/ne/ated
deta//iled
deli/g/hted
deth/r/oned
deno/min/ator
rota/v/irus
suri/na/mese

All the solutions my computer finds contain at least one of the following words, the last of which I think isn't even a word:

reticuled, depositum, reticella, citicorp

I'm not very happy with any of these, so the next question is what words are missing from my list...

[EDITED to add:]

So, I looked at all the words in solutions found by my program, and reclassified some of them that were inexplicably-to-me omitted from the smaller word lists, and added to the large list everything that was in the smaller ones. The best solution found is still that last one, except that maybe

RETREATED/DETAILER is better than RETREATER/RETAILER.

The same list of inevitable obscurities applies to the solutions I found. I suspect there are still some holes in my lists.