# A club for men only

Sixteen people tried to enter the local Club for Men Only this month. However, there is a precise rule that states who can be admitted to the club: of course the candidates can't know the rule before entering the club, so eight of them were rejected.

Here are the people who were admitted:

And these are the ones that were not admitted:

What is the requirement to enter such exclusive Club?

Credits: I created the avatars using avatarmaker.

Hint 1:

As stated in the title, this club is for men only. This means that it makes no sense to apply the admittance rule for (most) women. Or at least the evaluation will be too trivial.

Hint 2:

As already leaked by @Steve in the comments, names definitely matter: they are not just labels to refer the pictures. However, if you really want to be admitted in this club you won't necessarily have to change your name: you can also...

Hint 3:

..cut and/or grow your beard or hair. In some cases (Eduardo, Franklyn, Matthew) cutting beard/hair is not enough and the only option is growing one and cutting the other. If you are bald it could be the case that you cannot enter the club for good.

Hint 4

Only two letters of the names matter.

Hint 5 (definitive)

The requirement is not just about the name and/or the facial hair coverage. It is something about some kind of relationship between the two. The length of the hair and beard of the candidate is measured and somehow "compared" with (two letters of) their names.

• Are the names relevant, or are they just labels to allow us to refer to the pictures? – Steve Jun 9 '20 at 16:52
• @Steve I wanted to add this information in the next hint: names are definitely relevant – melfnt Jun 9 '20 at 17:31
• Is knowledge actually aplicable here? – athin Jun 12 '20 at 1:16
• @athin no, solving this puzzle only requires basic common knowledge – melfnt Jun 12 '20 at 6:32

I think the rule is as follows

Look at the first and last letters of the man's name.

If the first letter comes before the last letter in alphabetical order then the man is admitted only if he has more hair on the bottom half of his face than the top half. If, instead, the first letter comes after the last letter then the man is only admitted if he has more hair on the top half of his face.
If both letters are the same then the man must have the same amount of hair in the top and bottom half of his face.

Note: Here I am not considering hair on the back of someone's head, just the hair we can see in the picture.

Examples

Charis $$\rightarrow$$ C comes before S $$\Rightarrow$$ bottom half must be hairier than top half.
Earle $$\rightarrow$$ E is the same as E $$\Rightarrow$$ bottom half must be same hairiness as top half.
Hershel $$\rightarrow$$ H comes before L $$\Rightarrow$$ bottom half must be hairier than top half.
Marty $$\rightarrow$$ M comes before Y $$\Rightarrow$$ bottom half must be hairier than top half.
Mohammad $$\rightarrow$$ M comes after D $$\Rightarrow$$ top half must be hairier than bottom half.
Robin $$\rightarrow$$ R comes after N $$\Rightarrow$$ top half must be hairier than bottom half.
Ryan $$\rightarrow$$ R comes after N $$\Rightarrow$$ top half must be hairier than bottom half.
Ying $$\rightarrow$$ Y comes after G $$\Rightarrow$$ top half must be hairier than bottom half.

Craig $$\rightarrow$$ C comes before G $$\Rightarrow$$ bottom half must be hairier than top half.
Eduardo $$\rightarrow$$ E comes before O $$\Rightarrow$$ bottom half must be hairier than top half.
Franklyn $$\rightarrow$$ F comes before N $$\Rightarrow$$ bottom half must be hairier than top half.
Gene $$\rightarrow$$ G comes after E $$\Rightarrow$$ top half must be hairier than bottom half.
Josiah $$\rightarrow$$ J comes after H $$\Rightarrow$$ top half must be hairier than bottom half.
Matthew $$\rightarrow$$ M comes before W $$\Rightarrow$$ bottom half must be hairier than top half.
Miguel $$\rightarrow$$ M comes after L $$\Rightarrow$$ top half must be hairier than bottom half.
Sanford $$\rightarrow$$ S comes after D $$\Rightarrow$$ top half must be hairier than bottom half.

• This also checks out with Hint 3 since rot13(Rqhneqb, Senaxyla, naq Znggrj'f svefg yrggref pbzr orsber gurve ynfg yrggref naq gurl unir ab orneqf, gurersber vg jbhyqa'g or rabhtu whfg gb funir gurve urnq, nf gurl'q nyfb unir gb tebj n orneq) – Michael Moschella Jun 24 '20 at 16:52
• Well done as usual! In my wordings (as OP): rot13 (Gur eryngvir beqrevat orgjrra gur yratgu bs unve naq orneq zhfg or gur fnzr nf gur bar orgjrra gur svefg naq ynfg yrggre bs gur anzr) – melfnt Jun 26 '20 at 6:29
• You are right: only the rot13 (Beqrevat pbhag, abg gur inyhrf) – melfnt Jun 27 '20 at 7:10
• @melfnt Ah, sorry I misunderstood your comment, will delete my previous comment. – hexomino Jun 27 '20 at 8:29

New attempt: (previous attempt was based on the assumption that names have no role, so I didn't keep it)

Per Hint 2,

if we tally up the values of each person's name and the number of their divisors, we have this chart

We may observe from the admitted group:

1. the higher the divisor the more coverage of facial hair; 2, a divisor of 6 means all around coverage of either mustache (Muhammad) or hair (Hershel); 3, a divisor of 2 means you have to be bold (Earle) and; 4, a divisor of 4 means coverage of about half of the face (Charis and Marty has the bottom half; Robin & Ryan the top half; nothing on the opposite half).

Explanation of the rejected group:

Craig (4) should have chosen either Charis' or Robin's style; Eduardo (6) should have been like Hershel; Franklyn & Gene & Miguel (2) needs to be like Earle; Josiah (4) should cut the top patch & trim the circle beard; Matthew (4) lacks the top patch that get Ying admitted; Sanford (4) needs to get rid of the circle beard and connect his sides...

This interpretation also goes well with hints 1 & 2:

Whereas Hint 2 suggests changing hair coverage to adapt to the divisor values of one's name, for most ladies that is just not viable. Most women have much more hair than this.

• Interesting, but not the intended answer – melfnt Jun 9 '20 at 5:22
• Isn't "beard between the nose and upper lip" called "mustache"? – justhalf Jun 9 '20 at 11:42
• (comment to the new attempt): nice try again, but this is still too difficult with respect to the intended solution – melfnt Jun 15 '20 at 9:06

In order for the 8 men to be admitted their names have to contain at least two of the same letter.

1. Matthew

2. Enduardo

3. Franklyn

The above three have to cut their hair and grow a beard.

1. Gene