How can a nozir fulfill the mitzvah of drinking four cups of wine at the passover seder?
p.s. It is not a riddle. My son asked me this question, and I don't know what to answer him.
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If he can indeed drink wine for this purpose (as per the sources cited in WAF's answer and the comments there), then that's that.
Otherwise, though: there are opinions that even for the Four Cups one can use chamar medinah (a beverage used as the national drink of importance, e.g., beer or mead) - Rema to Shulchan Aruch, Orach Chaim 483:1. Now, a nazir is permitted to drink those; he's prohibited only to consume grape products. So he might be able to use chamar medinah for his Four Cups.
This article, on a site which I've never heard of before today, lists many of the standard sources and their silence on this question, and adds that it is equally askable regarding kidush on shabas. It then concludes with a suggestion (in the name of a chain of Rebbes from Lubavitch) that since mitzvos lav lehanos nitnu - the commandments were not given for derivation of pleasure - the wine that a nazir drinks to fulfill his obligation on the night of Pesach is not included in the prohibition against his [pleasurable] drinking of grape products.
It is a 'מחלוקת ריב''ן ותוס in .נזיר ד. Rivan says that being that person is already חייב in קידוש before he accepts נזירות, he still has to make קידוש. Tos' say that the part of קידוש that is on wine is דרבנן, and therefore he would not make קידוש.
If the 4 cups are דאורייתא, it has the same מחלוקת as the above. If it is דרבנן, all would agree that a נזיר would not drink.
Yerushalmi Nazir 6:5 quotes the opinion of R' Yossi HaGelili that a Nazir may not drink Ma'aser Sheini wine. He derives this from Bamidbar 6:3, which says both "wine" and "strong drink," which he finds repetitious (as wine is a strong drink). He therefore learns that the repetition is "to make wine for a Mitzvah like optional wine." So, no, a Nazir would not be able to have four cups of wine. He would be able to have four cups of a chamar medinah, though, as Alex noted.
The question, as asked, is simple to answer: Passover is a command (Le 23:5-8) while a Nazir's vow, was a mere personal vow. No Israelite had the authority to make a vow that supplants a command. The better question is, was Samson required to abstain from all wine, including Passover wine? It seems the answer, in this case, would be that Samson had to abstain, since he received a direct command with a specific commission (Jg 13:3-5).