4 TINFO 240 students are stuck in Bryan Goda\'s detention class and are only all

Question

4 TINFO 240 students are stuck in Bryan Goda's detention class and are only allowed to look towards the front of the class. They are not allowed to turn around or move, nor are they allowed to talk to each other. Student A is sitting in the back of the classroom and can see Students B and C. Student B is in front of Student A and can only see Student C. Student C is in front of Students A, B and there is a barrier between him and Student D, who is at the front of the class. Student D is at the front of the class, but no one can see him because of the barrier. He cannot see any of his fellow students. 2 students are given white hats and 2 students are given black hats. They cannot see the color of the hat they are wearing. Bryan Goda tells them that they are told to shout out the color of their they are wearing when they are certain. Who is the first person to shout out and why? A truth table may be useful.

Explanation / Answer

Among students A, B, C and D two students are given white hats and two students are given black hats. They cannot see the color of their own hats. A truth table can define the situation. Truth table is given below:

Situation

A

B

C

D

1

White

White

Black

Black

2

White

Black

White

Black

3

White

Black

Black

White

4

Black

White

White

Black

5

Black

White

Black

White

6

Black

Black

White

White

There can be 6 situations like the 6 rows in the truth table. If situation 3 or 4 occurs then student A can certainly tell his own hat color as in these situations A can see B and C both wearing same color of hats. But except situation 3 and 4, A cannot tell anything about his hat color. For situations 1, 2, 5, and 6 A cannot tell anything about its own hat color; observing this, student B can figure out that as A could not say anything about its hat color B and C must be wearing different colored hat. Hence in situations 1, 2, 5, and 6 B can certainly tell its own hat color observing the C’s hat color; in these cases B’s hat color would be different from C.

Hence for situation 3 and 4 the first person to shout out its own hat color would be A. For situations 1, 2, 5 and 6 first person to shout out its own hat color would be B.

Situation

A

B

C

D

1

White

White

Black

Black

2

White

Black

White

Black

3

White

Black

Black

White

4

Black

White

White

Black

5

Black

White

Black

White

6

Black

Black

White

White

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