You're a member of a new government with exotic rule-sets.

One of the rules governs when and how hair shall be cut. The law states that on the second Thursday of every month hair shall be trimmed, and it shall be trimmed in the following manner:

All the citizens shall be lined up alphabetically (last name, first name). Going from the front of the line to the back, the following shaving rules shall be applied fairly to all citizens.

If everyone in front of you is bald, you shall be shaved bald. If this is not true one of two things can happen.

If you are bald you will be given a wig to hide your shame. If you have hair it shall be permed to appear more wig like.

You are fourth in line and have immaculate hair. If the hair states of the other contestants are randomized, what is the most common hair style you will be left with? What percent chance is that?

  • $\begingroup$ Is a man with a wig on considered bald? $\endgroup$
    – Ben
    Feb 24 '16 at 20:35
  • $\begingroup$ it's a simple mathematical probability question... $\endgroup$
    – manshu
    Feb 24 '16 at 20:36
  • $\begingroup$ @Ben No, the bald shame is hidden from the world. The government has made their hair whole. $\endgroup$
    – DiscOH
    Feb 24 '16 at 20:37
  • 2
    $\begingroup$ Inspired by this? $\endgroup$
    – f''
    Feb 24 '16 at 20:44
  • 1
    $\begingroup$ If this had an interesting answer, I might consider it a good question. As it stands, it's akin to a grade-school nitpick, not a puzzle. $\endgroup$
    – GentlePurpleRain
    Feb 25 '16 at 18:15

Assuming the law of the land accounts for vacuous truth:

You will be shaved 100% of the time. For the first person in line, "Everyone in front of you is bald" is vacuously true, and so they will be shorn. Then the second has only a bald individual in front of them, and so on all the way down.

  • $\begingroup$ this answer is right if they go down the line front to back. The question is kind of ambiguous $\endgroup$
    – Slepz
    Feb 24 '16 at 20:35
  • $\begingroup$ @Slepz, good point. Updating the question to reflect intent. $\endgroup$
    – DiscOH
    Feb 24 '16 at 20:38
  • $\begingroup$ from the puzzling point of view "everyone in front of you is bald" is ambiguous. It could mean "There is no-one in front of you with hair or a wig" or it could mean "there are people in front of you, all of whom are bald." Relying on a strictly mathematical interpretation of the sentence, and using a mathematical term for that without link or explanation, suggests this is not a puzzle at all. That the OP accepted this answer cements that. Not a puzzle. $\endgroup$ Feb 26 '16 at 13:26

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