You are a contestant on a game show. You have three closed doors in front of you. One of the doors has a car behind it and the other two doors have nothing. You have to choose a door to open.
You have with you a Magic Watch.
- Whenever you ask the watch a question with a yes/no answer, it will blink either red or blue.
- One of the colors represents 'yes' and the other 'no'.
- You don't know which color means what. (gotcha!)
- You are allowed to ask the watch only 2 questions before you make your decision.
Which questions would you ask and how would you choose the door to open?
The puzzle might have a number of solutions and this is one of them.
Solution:
The contestant should ask the following two questions:
1) If I asked whether the car was behind door 1, would you blink red?
2) If I asked whether the car was behind door 2, would you blink red?
There are two cases here:
a) red = no, blue = yes:
The watch can answer in 4 different ways:
1) red, blue:
From the answer to the 1st question, car is behind door 1.
From the answer to the 2st question, car is not behind door 2.
2) blue, red:
From the answer to the 1st question, car is not behind door 1.
From the answer to the 2nd question, car is behind door 2.
3) blue, blue:
From the answer to the 1st question, car is not behind door 1.
From the answer to the 2nd question, car is not behind door 2.
4) red, red:
From the answer to the 1st question, car is behind door 1.
From the answer to the 2nd question, car is behind door 2.
b) red = yes, blue = no:
The watch can answer in 4 different ways:
1) red, blue:
From the answer to the 1st question, car is behind door 1.
From the answer to the 2st question, car is not behind door 2.
2) blue, red:
From the answer to the 1st question, car is not behind door 1.
From the answer to the 2nd question, car is behind door 2.
3) blue, blue:
From the answer to the 1st question, car is not behind door 1.
From the answer to the 2nd question, car is not behind door 2.
4) red, red:
From the answer to the 1st question, car is behind door 1.
From the answer to the 2nd question, car is behind door 2.
Observe that the conclusions are exactly the same for the same answer set irrespective of the color code.
Hence, when the watch answers:
1) red, blue: Pick door 1.
2) blue, red: Pick door 2.
3) blue, blue: Pick door 3.
4) red, red: This outcome is impossible since it implies that the car is behind door 1 as well as door 2.
Subodh Singh almost got the answer! Brilliant!
I think this is the toughest puzzle on this blog.
ReplyDeletemy brain farts
even I agree. too difficult
ReplyDeleteIf doors 1 & 2 are blank, will you show 'Red'?
ReplyDeleteRed
Door 3 has the car
Blue
Does 2 contain the car?
Red
1 contains the car
Blue
2 contains the car
Agreed that if the watch blinks Red to the question "If doors 1 & 2 are blank, will you show Red?", then the car is behind door 3. But if it blinks Blue, how does the second question help you decide?
ReplyDeleteWe learn two things from the answer to the first question.
ReplyDelete1. Whether 3 has the car.
2. Whether Red means 'True'
The answer to the second question tells you whether the car is behind 2.
Since you already know the meaning of the color at this point you can easily infer the veracity of the second blink and answer accordingly.
How do we know whether red means true from the answer to the first question?
ReplyDeleteMy second question should have been the same as the first one except for pointing to the second door.
ReplyDelete