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The following words have a hidden but very distinguished property that allows to order them in a very natural way:

pins up iron sigma eyes another ball face sum monkeys

What is the very distinguished property of these words?
What is the resulting ordering?

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  • $\begingroup$ Requesting a hint: Are there any more words in the English language that could be added to this list? $\endgroup$ – Mark Mar 17 '15 at 17:05
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    $\begingroup$ @Mark: If suffixes were allowed, you could go with "Oceans", "o'clock", and "Apollo" for the next three. $\endgroup$ – Joe Z. Mar 17 '15 at 18:03
  • $\begingroup$ This was a good puzzle. Nice job! $\endgroup$ – Joe Z. Mar 17 '15 at 18:06
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I believe the answer is

Another Face Sum Eyes Monkeys Sigma Up Ball Iron Pins

The property is that these words can be prefixed with numbers to create expressions:

One Another (an expression meaning "each other")
Two-Face (Harvey Dent, a villain in Batman)
ThreeSum (the 3SUM problem)
Four-Eyes (an insulting term for somebody who wears glasses)
Five Monkeys (little ones, jumping on the bed)
Six Sigma (a statistical standard for process consistency)
Seven-Up (a drink or a children's party game)
Eight Ball (a fortune-telling device, or a billiards game)
Nine-Iron (a type of golf club)
Ten Pins (in bowling)

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  • $\begingroup$ My only issue with this is your answers for "ball" and "iron". Not sure how to say this without giving it away for someone not looking at spoilers, but there are a lot of other "irons" that have different categorization. Similarly for "ball" in one of your contexts (but not the other). $\endgroup$ – Duncan Mar 17 '15 at 18:11
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    $\begingroup$ They're the numbers most commonly associated with those words, though, so I went with it. $\endgroup$ – Joe Z. Mar 17 '15 at 18:11
  • $\begingroup$ I totally get it. I guess it's not an issue with your answer specifically - the answer totally makes sense. It's just that if it's the answer, I think the "iron" one specifically isn't specific enough. I agree with you, though, it's a good puzzle. $\endgroup$ – Duncan Mar 17 '15 at 18:45
  • $\begingroup$ The iron one may not be specific enough, but it is the only one left after all the other answers are placed. $\endgroup$ – Joe Z. Mar 17 '15 at 18:51
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The following is just a minor comment on the solution of Joe Z.

Counting does not necessarily start at one, but may also start at zero (for instance, Ernst Zermelo used this variant). This then allows the following side solution (the differences to Joe Z's solution are shown in boldface):

Zero-sum (a special type of game in game theory)
One another (each other; copied from Joe Z.)
Two-face (Harvey Dent, a villain in Batman; copied from Joe Z.)
Three monkeys (the three wise monkeys)
Four-Eyes (an insulting term for somebody who wears glasses; copied from Joe Z.)
Five Iron (golf club that has a relatively narrow metal head)
Six Sigma (a statistical standard for process consistency; copied from Joe Z.)
Seven-Up (a drink or a children's party game; copied from Joe Z.)
Eight Ball (a billiards game; copied from Joe Z.)
Nine-pins (European bowling game)

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  • $\begingroup$ Nice job shifting them over. $\endgroup$ – Joe Z. Mar 18 '15 at 15:37

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