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rsl12 · 08-17-2004, 06:00 PM

OK, I will get to my solution, but first, i will show that you have to ask at least one question that has the potential to be unanswerable as "yes" or "no". Why? If you only ask questions that are definitely answerable with a yes or no, there are only two possible things that happen--both questions result in the same color flashing, or each of the two questions results in a different color flashing. It doesn't matter if you have two yellows or two blues--they both mean the same to you. It also doesn't matter if you get blue then yellow, or yellow then blue. Those two results also mean the same to you, since blue and yellow, as colors, carry no information by themselves. So only two possible occurences will happen when you ask your two questions. HOWEVER, there are 3 doors. You need at least 3 unique, distinguishable outcomes to occur in order to determine which of 3 doors to open. Therefore, asking questions that are always answerable as yes or no will NEVER work.

(Someone might argue that one of the questions could somehow happen to reveal which color is true and which is false, and then you would have 4 unique answers, which would be more than sufficient. HOWEVER, if you try and determine which color stands for which at the same time as trying to figure out which door to open, that leads to 2x3=6 possible outcomes!! (eg, outcome 1: door #1 and blue means yes. outcome 2: door #1 and blue means no. etc etc.) this is simplifying things a bit--there are other possibilities, but I think it's impossible to get a sufficient # of answers.)

THEREFORE, here's my approach. It assumes that the watch does something crazy if you ask it a question that it can't answer yes or no--blinks both lights, doesn't blink at all, something. It also assumes that the goats are identical in every way, that you don't like one goat more than another, and kismet doesn't lead to you getting some fabulous girl as a result of the wind current caused by opening door 1 instead of #2. Also, instead of questions, I'm using statements, because I couldn't figure out how to frame the statements into appropriate questions. I know this is cheating.

Statement 1. "Blink the color for yes if I would prefer what's behind door #1, and blink the color for no if I would prefer what's behind door #2."

(If it goes crazy, the car is behind door #3. Otherwise, there's a goat there.)

Statement 2. "Blink the color for yes if I would prefer what's behind door #2, and blink the color for no if I would prefer what's behind door #3."

(If it goes crazy, the car is behind door #1. Otherwise, there's a goat there, and the car is behind door #2.)

08-17-2004, 06:00 PM	#2 (permalink)
rsl12 On the lam Location: northern va	OK, I will get to my solution, but first, i will show that you have to ask at least one question that has the potential to be unanswerable as "yes" or "no". Why? If you only ask questions that are definitely answerable with a yes or no, there are only two possible things that happen--both questions result in the same color flashing, or each of the two questions results in a different color flashing. It doesn't matter if you have two yellows or two blues--they both mean the same to you. It also doesn't matter if you get blue then yellow, or yellow then blue. Those two results also mean the same to you, since blue and yellow, as colors, carry no information by themselves. So only two possible occurences will happen when you ask your two questions. HOWEVER, there are 3 doors. You need at least 3 unique, distinguishable outcomes to occur in order to determine which of 3 doors to open. Therefore, asking questions that are always answerable as yes or no will NEVER work. (Someone might argue that one of the questions could somehow happen to reveal which color is true and which is false, and then you would have 4 unique answers, which would be more than sufficient. HOWEVER, if you try and determine which color stands for which at the same time as trying to figure out which door to open, that leads to 2x3=6 possible outcomes!! (eg, outcome 1: door #1 and blue means yes. outcome 2: door #1 and blue means no. etc etc.) this is simplifying things a bit--there are other possibilities, but I think it's impossible to get a sufficient # of answers.) THEREFORE, here's my approach. It assumes that the watch does something crazy if you ask it a question that it can't answer yes or no--blinks both lights, doesn't blink at all, something. It also assumes that the goats are identical in every way, that you don't like one goat more than another, and kismet doesn't lead to you getting some fabulous girl as a result of the wind current caused by opening door 1 instead of #2. Also, instead of questions, I'm using statements, because I couldn't figure out how to frame the statements into appropriate questions. I know this is cheating. Statement 1. "Blink the color for yes if I would prefer what's behind door #1, and blink the color for no if I would prefer what's behind door #2." (If it goes crazy, the car is behind door #3. Otherwise, there's a goat there.) Statement 2. "Blink the color for yes if I would prefer what's behind door #2, and blink the color for no if I would prefer what's behind door #3." (If it goes crazy, the car is behind door #1. Otherwise, there's a goat there, and the car is behind door #2.) __________________ oh baby oh baby, i like gravy.