re: The Nine Puzzle.

Investigating the research, I came across the work of Neave and Shields (2008) on the effects of facial hair on women's perceptions of men's attractiveness, masculinity, and dominance. The researchers asked female participants to rate various male faces of average attractiveness. The faces were digitally altered to show different degrees of facial hair—clean-shaven, light stubble, heavy stubble, short beard, or full beard. For each alteration, women were asked to rate the face's masculinity, aggression, dominance, attractiveness, and social maturity. Participants were also asked to indicate their own desire for the male as a short- and long-term partner.

The results indicated that the women found men with light stubble most attractive; these men were preferred as both short- and long-term partners. However, the women perceived male faces with full beards as the most masculine, aggressive, and socially mature; the women also thought these men looked older. Men's faces with light beards were considered the most dominant.

Research by Dixson and Brooks (2013) used similar procedures and recorded judgments by both men and women on the faces of men with varying degrees of facial hair. As in the first study, women found stubble on men most attractive, (In this study, the stubble was heavier.) Nevertheless, women rated men with full beards as the highest for perceived parenting ability and healthiness. Overall, as facial hair increased, women's ratings of masculinity increased, too—particularly for women who reported being at the fertile phase of their menstrual cycle. Men had similar judgments of facial hair, except that they found full beards as appealing as heavy stubble. Men also noted a greater perception of masculinity as facial hair increased.

Overall, these ratings suggest that an intermediate level of facial stubble is more attractive for a sex partner, while a fuller beard is perceived as indicative of someone with good fathering ability and more investment in offspring.

Given the results, whether a man should grow a beard will depend on his own relationship goals (and perhaps those of his preferred partner). Guys looking to get noticed and be more sexually appealing may benefit from some masculine stubble on their cheeks (especially when combined with being nicely dressed and otherwise well-groomed). Add some sexy eye contact, flirtatious touching, and the right conversation topics, and a man may reignite the passion of his long-term partner—or attract the interest of somebody new.

Men in comfortable, long-term relationships—or looking to find one—may benefit from a full-bearded look. This is especially true if he wants to be seen as the fatherly type ready to settle down with a family; a full beard has the added benefit of making a man look more healthy, masculine, and trustworthy. A beard can also help a man build rapport with a partner, demonstrate a positive personality, and stand out from the crowd. (Just remember to trim it down a bit.)

There is a contingent of women who do not care for men's facial hair at all, so for men committed to smooth cheeks, there's certainly someone out there for you, too. But fundamentally, as with other mating cues, women's preferences in men are often linked to the type of relationship and gender dynamic they want. By changing his facial hair, a guy may be more likely to attract the type of relationship partner he seeks.