MATH SOLVE

5 months ago

Q:
# Five students are seated in a circle. Each student has either a red disc or a green disc painted onher forehead. Each student can see the other four discs, but not her own. If a student is wearing a green disc, any state she makes is true; if she is wearing a red disc, any statement she makes isfalse.Student 1 says: I see 3 green and 1 red discsStudent 2 says: I see 4 red discsStudent 3 says: I see 1 green and 3 red discsStudents 4 say: it is raining outsideStudent 5 says: I see 4 green discsWhich students have green discs and which students have red discs?

Accepted Solution

A:

Answer:Students 3 and 4 have green discs. Students 1, 2, and 5 have red discs.Step-by-step explanation:If Student 1 is telling the truth, Students 2 and 3 must be lying. If that were true, Student 1 would see at least 2 red discs, not 1. So Student 1 is lying, and therefore has a red disc.Therefore, Student 5 is also lying, and must also have a red disc.If Student 2 is telling the truth, the other four students must be lying. That means Student 2 would have a green disc, and the other four would have red discs. But if that were true, then Student 3 would be telling the truth. Therefore, Student 2 is lying.So far, we know Students 1, 2, and 5 are lying. If Student 3 is telling the truth, then she and Student 4 each have a green disc. If Student 3 is lying, then all five students would have red discs, which would mean Student 2 was telling the truth.Therefore, Students 3 and 4 have green discs. Students 1, 2, and 5 have red discs.