ManWithAPlan

You have a very nice, shiny watch. But this is no ordinary watch. This watch can answer two yes or no questions 100% accurately per day You ask, and either a blue or yellow light will flash. Unfortunatley, you don't know which light means yes and which light means no, and you can never find out because there's a 50-50 chance of the lights switching every night.

You happen to be on a game show. The rules are simple. There are three doors. Behind two are goats. Behind one is a shiny red car. Obviously, you want the car. You can choose any door, after asking the watch two questions.

So tell me, What are two questions you can ask so that you will have a 100% chance of getting the car? Remember, it has to work EVERY TIME



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i don't know the answer yet, but i think i've stumbled onto something...

to solve it, it does not matter which is yes, you just have to use the answers to gain two possible scenarios, (if a then b ) (if not a then not b) or (if a then not b) (if not a then b)

i think that one of the scenarios always has to come out false so you can eliminate it (or you get two possible answers)

the first choice should not automatically eliminate either a negative or affirmative answer for the second one (are the goats together? and are the goats on the ends))


NOTE: these are just hypotheses, not absolute facts because i havn't gotten the answer yet.


finally here is a crude little chart to help us figure it out.




[O] [X] [X]
[X] [O] [X]
[X] [X] [O]

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In the end we are but wisps

rsl12

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.)

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ManWithAPlan

questions.... not orders...


my friend came up with this and it seems to work.


Q1. If I asked if the car was behind door 1, would you flash yellow?
Q2. If I asked if the car was behind door 2, would you flash yellow?

If blue was yes and it was
yellow, blue - car is behind 1
blue, yellow - car is behind 2
yellow, yellow - car is behind 3

if yellow was yes
Yellow, Blue - car behind 1
Blue, Yellow - car behind 2
blue, blue - car behind 3

__________________
In the end we are but wisps

rsl12

yow! i stand corrected. that part where i said "it's simplifying things a bit"...that was where I was trying to come up with something like that, and just passed it up as impossible.

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oh baby oh baby, i like gravy.

orphen

yeah this works because if you translate into:

if yellow were YES
:::: If I asked if the car was behind door X, would you say yes? (flash yellow)
and if the watch answers YES (flashes yellow) it means the car is behind it.
or simplified: is the car behind door 1? yes.

if yellow were NO
:::::If I asked if the car was behind door X, would you say NO? (flash yellow)
and if the watch answers NO (flashes yellow) it again means the car is behind it
or simplified: is the car NOT behind door 1? NO


Thus is you ask that question, regardless of yellow being yes or no, you can decern the answer

kudos to your friend.

neekap

Eegads... I think my brain just exploded. :-P

Crack

Sell the watch for a butt-load of money on ebay, then buy yourself a shiny car and a house!

Come on folks... its not rocket surgery here!

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Crack, you and I are long overdue for a vicious bout of mansex.

~Halx

fuqnbastard

it's the same as the two-guards riddle, for example http://able2know.com/forums/about26261.html

RespectThat

no....lol
besides..the guard riddle has no answer

aKula

ok theres a similar one in a book i read called 'the curious incident of the dog in the nighttime'. Same show. You choose one door, then the host opens a different door and reveals that there is a goat behind it. The host then gives you the choice of changing the door you picked. Should you stay with your choice or switch doors?

filtherton

Switch, odds favor the switch.

telekinetic

The answer to that one is almost trivial: ask the guard "What would you say if I asked you if this were the door to freedom?"

There is a 66% of hitting the prize if you switch, compared to a 33% chance if you don't. Always switch. Thread about switching doors: http://www.tfproject.org/tfp/showthread.php?t=37188

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twisted no more

itch vaccine

Good answer "ManWithAPlan's friend"

summerkc

Why not just use the watch to bet on stuff? Are the Colts going to win the Superbowl? Yes!