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## Math for fun and glory

### Course: Math for fun and glory>Unit 2

Lesson 1: Brain teasers

Do not watch before Blue Forehead Room. THIS IS THE SOLUTION! Created by Sal Khan.

## Want to join the conversation?

• Could they have talked? If so, wouldn't the most logical solution be to turn to the person next to you and say, "Your forehead is ___?" rather than sit through 100 rounds of this? If talking is not on the table, would this is a very logical and safe approach.
• its a silent room, no forms of communication allowed, it would have to be or else this whole thought process would be worthless and I would have to regret watching the videos, common people
• If I put saliva on my forehead then the color will come on my hand so I can easily find out. Is that also a solution?
• Good out of box thinking. In real life, such thinking may just be the solution to a seemingly daunting challenge. But here, in a carefully controlled logical problem, you assume you can't do such things.
• After the first lights, nobody would leave the room because they see 99 people with blue heads and assume they are not blue. After the second lights, they will see nobody had left the room. However, since they know, say, the 2nd person also sees 98 people with blue foreheads (you assume you are not blue), and he assumes he is not blue either, he will not leave. And this will go on for everybody and nobody would actually leave.

Explain please? (Could you give an example with at least 5 people. It does not seem to work after 3 people)
• Ok. 5 people, all blue, but they don't know:

We go into the head of one---

First time: Ok, the other 4 are all blue, but what if mine is the only not-blue? (He doesn't leave)
Second time: They're not leaving because they all don't know for certain that theirs are blue---using the logic of the two people example, but I still do not know that mine is blue. (He doesn't leave)
Third time: Same as second time, since there are more than two blues, no one can leave. (He doesn't leave)
Fourth time: Ok, now there must be at least four blues (which he can see), and now they know it. So if they all leave this time, he himself must not be blue. If they don't leave, then they must also see four other blues and have yet to determine their own color. (He doesn't leave)
Fifth time: Since no one left, we know that there are more than four blues, which means that everyone is blue, and now they can determine it for certain. (They all leave)
• How would they know to count how many times the light is turned off? Is this part of the perfect logician thing?
• i think u cant count the times the light is turned off
(1 vote)
• when you see a persson with a blue forehead stare at them. If they stare back they notice you have one too.
If the person you stare at is already doing it to someone else you satre to a different person.
• The other logicians will just find you creepy and run out of the room. Then you can deduce that you do not have a blue forehead
• Couldn't you just wipe the paint off your forehead to see what color it is?!?!?!?!?
• They let the paint dry.
• At , after the two blue foreheads walk out, why wouldn't the last person in the room, even though he saw that he didn't have blue earlier, now assume that he DOES have blue because he is to only dude left in the room? Just wondering.
• Since he's the only person left in the room, there would be nobody else to compare with and that leaves a tiny chance of his forehead being painted blue.