POW#6 Spring 2022
Solutions due by noon on Friday, March 25
Three rebels calling themselves Rogue Zero try to steal the Death Star plans, and get caught by Darth Vader. The rebels plead for their release, and Darth Vader decides to give them a chance. Darth Vader tells the rebels that there are three black helmets and two white helmets. Then the rebels are seated in a line facing a wall, and they are told that they cannot look behind.
Wall --- Rebel #1 --- Rebel #2 --- Rebel #3
Rebel #1 can only see the wall, Rebel #2 can see Rebel #1 in front, and Rebel #3 can see both Rebel #1 and Rebel #2. Darth Vader says that he will place a random helmet on each of them, and that he will let anyone who can tell their helmet color correctly will be set free. Otherwise, they will be sent to an imperial labor camp. Keep in mind that a rebel cannot see the color of the helmet he/she is wearing.
After a few minutes, Darth Vader asks all the rebels if any of them can identify the color of their helmet. Unfortunately, Rebel #3 says that he/she cannot tell the color of his/her helmet. Then, Rebel #2 also says that he/she cannot tell the color of his/her helmet. Finally, Rebel #1 says that he/she knows what color his/her helmet is. Darth Vader confirms that Rebel #1 does indeed know the correct color of his/her helmet, and sets him/her free.
How did Rebel #1 know the color of his/her helmet? Provide the color of his/her helmet, and a logical explanation how Rebel #1 could have identified it correctly.
This problem is brought to you by Prof. Choong-Soo Lee.
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