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It is forbidden to take a haircut on Chol ha'Mo'ed in order to encourage people to take a haircut prior to Yom Tov, and won't start the Yom Tov looking unkempt.
If a worker [that has a high public profile] loses an object on Erev Yom Tov and was unable to take a haircut it remains a question to the Gemara whether he may take a haircut on Chol ha'Mo'ed. (1)
A person that arrives back from an overseas trip on Chol ha'Mo'ed may take a haircut according to the Chachamim. Rebbi Yehudah says that it is forbidden to take a haircut if the trip was for the purpose of making extra money. (2)
According to one version, Shmuel says that an infant that was born on the Mo'ed may take a haircut on Chol ha'Mo'ed. According to another version, Shmuel says that all children may take a haircut on Chol ha'Mo'ed.
The regulations of the mourning period do not apply on Yom Tov. (3)
It remains a question to the Gemara whether the regulations of an excommunicated person apply on Chol ha'Mo'ed.
The regulations of a Metzora apply even on Yom Tov. (4)
A mourner is prohibited from taking a haircut.
A BIT MORE
1. If a public worker such as a barber loses an object, it becomes public knowledge. Therefore an exception may be made in his case and he may be allowed to take a haircut on Chol ha'Mo'ed. However no exception can be made for a regular person because of the concern that people will not know the reason for the leniency.
2. If a person traveled overseas for the purpose of making a livelihood, Rebbi Yehudah agrees that if he arrives back on Chol ha'Mo'ed he may take a haircut. If he traveled oversees for tourism, everybody agrees that it is forbidden to take a haircut even if he arrives back on Chol ha'Mo'ed.
3. The regulation of mourning is an individual Mitzvah and is supplanted by the public Mitzvah of being joyous on Yom Tov.
4. The Gemara deduces from the Halachos of a Kohen Gadol that the regulations of a Metzora apply on Yom Tov. The regulations of a Metzora apply to a Kohen Gadol even though for a Kohen Gadol the entire year has the same status of a Yom Tov.
The Ra'avad says somebody who arrived from overseas after going on a sightseeing trip is only prohibited to take a haircut if he went from Eretz Yisrael to Chutz la'Aretz. Since he transgressed the prohibition of leaving Eretz Yisrael for the purpose of sightseeing, it is not permitted to take a haircut when he arrives on Chol ha'Mo'ed. However if somebody traveled within Eretz Yisrael or within Chutz la'Aretz, it is permitted to take a haircut if he arrives back on Chol ha'Mo'ed. The prohibition of Rebbi Yehudah regarding somebody who went overseas for the purpose of making extra money also only applies if the trip was from Eretz Yisrael to Chutz la'Aretz . (Tur, Beis Yosef)
It is forbidden to take a haircut on Chol ha'Mo'ed even if one took a haircut before the Mo'ed. Even if an avoidable occurrence stopped you from taking a haircut prior to the Mo'ed it is nevertheless forbidden to take a haircut on Chol ha'Mo'ed. If an illness did not allow you to take a haircut prior to the Mo'ed it is likewise forbidden to take a haircut on Chol ha'Mo'ed. (Shulchan Aruch OC 531: 1,2,3)
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