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These ten words are arranged in order according to a certain property they share:

festive
fixture
salient
resolving
recline
accessory
advise
headlight
redcoat
programming

Where should each of the following four words be inserted into the list?

abbreviate
twelve
humdinger
anecdote

What is the property shared by all fourteen words?

Hint

A word's meaning is not relevant to the property in question.

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    $\begingroup$ In looking for a pattern among these words, I realised for the first time that the word "salient" has an alien in the middle! $\endgroup$ – Rand al'Thor Jul 14 '15 at 18:10
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    $\begingroup$ uh oh. rand's back. answer fast! :) $\endgroup$ – JLee Jul 14 '15 at 18:18
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    $\begingroup$ Wow, all 10 of the example words have 3 vowels (depending on your y-tolerance). Then only one of the additional 4 has 3 vowels... I wonder what the statistical odds of that are. $\endgroup$ – Going hamateur Jul 14 '15 at 18:25
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    $\begingroup$ Once the property is found, then sorting the list becomes trivial, or so I assume! :) $\endgroup$ – JLee Jul 14 '15 at 18:32
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    $\begingroup$ hmm, I can see a Festive Humdinger or a Salient Mixture. Maybe an Advice Accessory will help me find the pattern ;D $\endgroup$ – Nyk 232 Jul 14 '15 at 19:03
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That was a real humdinger. Now I'm feeling festive.

Roman numerals. Each word has, somewhere after the first character, a string of Roman Numerals, evaluating to a number. Let the property be that number. Then we get this ordering:
festIVe = 4
abbreVIate=6
fIXture=9
saLIent=51
tweLVe=55
resoLVIng=56
reCLIne=151
aCCessory=200
aneCDote=400
aDVIse=506
heaDLIght=551
reDCoat==600
huMDInger=1501
prograMMIng=2001

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    $\begingroup$ In that case, wouldn't mixture be 1009? $\endgroup$ – Zikato Jul 15 '15 at 13:14
  • $\begingroup$ he's looking past the first character, otherwise even the original order is wrong $\endgroup$ – dzastergamer Jul 15 '15 at 13:42
  • $\begingroup$ Nope, @Zikato is right. I goofed. I had fixture and changed it at the last minute. Argh! $\endgroup$ – dennisdeems Jul 15 '15 at 14:06

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