Red / Blue Dot?

There are several logical puzzles that impress me because they have a very good quality and made me think a lot before able to answer it. However I have one favorite puzzle that for me is a good one to test and figure out the smartest person among smart people. So this is the puzzle I mean (you may find it in many other sources because this puzzle is one of famous puzzle, I just re-write it):

A great philosopher wants to test who is the smartest among his students. There are 3 students and they are very very clever. So the great philosopher should make a test that is totally fair for them. It means that each students should have a same chance to answer the test.

So it is the test:

The great philosopher put a dot on each student forehead. There are 2 possibilities color of dot that will be used: red and blue. Each student should know the color of dot on the other student heads, but shouldn’t know his own color. The challenge is to figure out the color of dot in their own forehead.

After putting the dot, the philosopher will ask all students if they see at least one red dot on their friend’s forehead. If they see, they should raise up their hand.

So then the battle begin, each of students think deeply and logically to find out the color of dot in their head. The great philosopher actually put red dot to all of them. Sure he did this to make the test as fair as possible. If he put different color, the chance doesn’t same anymore for each student. But by having all red dot in all head, now he create a very fair test for his students. Now it will relay on his student’s logical thinking to answer this test.

This puzzle seems impossible to be answered, but that is the greatest point of puzzle, tomake the reader think that it’s unanswerable. But it has an answer. And the smartest student will be able to find it. How about you, if you are one of the students, can you answer it? No guessing of course, it should based on logical deduction.

After several time one of the students answer it. He say that his head have red dot. How can he find that out? This is how he thinks:

First, there is only two possible answer: red and blue.

Second, he sees that all students raise their hand, it means at least there are 2 red dots. He have seen 2 red dots, but it doesn’t guarantee anything, there is still 50-50 chance for red and blue on his head.

Third, he tries to think as his friend’s think. His friend will see 1 red dot and one on his head. If his friend see blue dot in his head, then it means his friend will instantly know that he (his friend) should have red dot. But it doesn’t happen. So the only possibility is that he has red dot.

Simple answer isn’t it? But I don’t think every person can catch this at the first time. Can you :D?

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