Magic Watch

[thisiskyle]

Maybe you've heard this one before. It took me some serious pacing to figure out.

You have a magic watch that always answers yes-or-no questions accurately by displaying either a red or a blue light. The catch is your only allowed two questions a day and the watch randomly switches between red=true and blue=true every morning. If you were on a game show where there were three closed doors, one of which had a fabulous prize behind it, what two questions could you ask your watch to guarantee victory?

[Richard_BenoitEnglipedia Drone]

This is a good one. I am still thinking and refuse to look it up. Feels like the good ol days when people who couldn't get the answer would spread it and bounce it off other people to see if they could answer it!

[Richard_BenoitEnglipedia Drone]

I proposed this to my wife on one of our long train trips. She spent about 30 minutes, on it on and off, then said.... It is impossible. It must be a trick.

I still don't know, and still refuse to look it up.

[thisiskyle]

I linked the solution because I'm a cruel temptress.
http://www.msu.edu/~irvankyl/webby/Magic%20Watch%20Solution.docx

[Richard_BenoitEnglipedia Drone]

Well it at least renews my interest, now that I know it actually is possible.

Give me a hint. For example is the answer abstract? Like a think outside the box answer? Or is it purely logical like a math equation?

Know what I am getting at?

[thisiskyle]

Hint: There is a category of questions you can ask the watch to which it will respond by showing the same color light regardless of whether the answer is yes or no. For instance: "Does blue correspond to 'yes'?" will always result in a blue light.

[Richard_BenoitEnglipedia Drone]

Ah ok! That hint was gigantic! I could ask a hypothetical question then. Like "If the prize is behind door number 1 will you shine blue?" Then if he shines red/blue I have trapped it into telling me two pieces of info?

[thisiskyle]

To answer your question as directly as possible: No, asking a one bit question will yield a one bit response.

[Richard_BenoitEnglipedia Drone]

Well to be fair that was a yes or no question I shall continue to grind then.

[thisiskyle]

My intention was (and is) to not put any value judgement on your question. By "one bit" I meant one piece of information: true/false, yes/no, heads/tails, on/off, 0/1. The watch is only capable of providing info one bit at a time. You can't "trick" it into giving you two.

[pakalikaPakalika]

how bout ask 2 questions in one, like is the car behind door 1 & 2 and blue true or is the car behind 2&3 and red true?

[Richard_BenoitEnglipedia Drone]

Yeah that isn't two bits of info is it? Just grouping the doors in pairs for both questions? For example "Is it behind either door one or two?"

[thisiskyle]

how bout ask 2 questions in one, like is the car behind door 1 & 2 and blue true or is the car behind 2&3 and red true?

To clarify, there is no car. The fabulous prize is well written English textbooks. How's that for motivation?

[Paul]

Maybe you've heard this one before. It took me some serious pacing to figure out.

You have a magic watch that always answers yes-or-no questions accurately by displaying either a red or a blue light. The catch is your only allowed two questions a day and the watch randomly switches between red=true and blue=true every morning. If you were on a game show where there were three closed doors, one of which had a fabulous prize behind it, what two questions could you ask your watch to guarantee victory?

At face value this question seems rather easy to me. If a red or blue light displays anytime during the course of asking your alloted two questions per day, anytime either light showed up would indicate a correct answer so you could ask a simple question;

1st question; Is there a fabulous prize behind door one? No light. (Thus eliminating door one.....or any door that you start with for that matter)
2nd question; Is there a fabulous prize behind door two? No light go to door three and get your prize.

Yes light for either first question of second question your answer is deemed correct and open corresponding door.

It can't be that simple now is it?

The color of the light should not matter, if a light shows an accurate answer no matter the question, ask the right question and the light will show.

[Richard_BenoitEnglipedia Drone]

1st question; Is there a fabulous prize behind door one? No light. (Thus eliminating door one.....or any door that you start with for that matter)
2nd question; Is there a fabulous prize behind door two? No light go to door three and get your prize.

Where does "no light" come from? I thought it was just blue or red. And you have no idea which is yes, and which is no.

[pakalikaPakalika]

Ok ok this question has just drag out toooooo long, can we just get the answer

[Paul]

1st question; Is there a fabulous prize behind door one? No light. (Thus eliminating door one.....or any door that you start with for that matter)
2nd question; Is there a fabulous prize behind door two? No light go to door three and get your prize.

Where does "no light" come from? I thought it was just blue or red. And you have no idea which is yes, and which is no.

Well if I am reading the OP correctly the watch only answers yes-no questions accurately, so if I asked a "wrong" or inaccurate question no light would appear on the watch.

I readily admit my examples were not very good, I put them there for an example.

I haven't read the link to the answer either.

[Paul]

Ok ok this question has just drag out toooooo long, can we just get the answer

Look at one of the previous posts, there is evidently a link to the answer in it.

[pakalikaPakalika]

There is, but it is in a different style word and I can not look at it with the computer at school. It is in word 2007 and school computer is word 2003. I keep saying look when I get home, but I always forget

[Richard_BenoitEnglipedia Drone]

As far as I could tell.

If you ask the watch:

"is the prize behind either of these two doors?" (1 and 2) (you get a color doesn't matter which red or blue)

Then ask:

"is it behind either of these two doors?" (2 and 3) (you would get the same or opposite color you got from the first question)

At which point you should be able to figure it out. Granted we are allowed such questions.

Does that work or make sense?

[Paul]

I dont follow, because either way the watch is going to flash one color or another or the same, the color really doesnt matter it seems to me.

If you ask 1 and 2, and the light goes off, then 2 and 3, and the light goes off. Which door would you open or think has the prize? It still could be 1, 2, or 3 couldnt it?

If could be a Yes or No light.

I am stuck on asking the right question that would eliminate a door rather than just getting a yes or no response.

[Richard_BenoitEnglipedia Drone]

This is what I was thinking. But as you mentioned Paul, without knowing what color red/blue represents it soon falls appart.

[Richard_BenoitEnglipedia Drone]

Ok well in the last 10 minutes I have given up. I searched google, and found an answer which the OP deemed as incorrect. (two bits of information) It seems to be the consensus of the internet community, so I would love to see the OP's answer, and how it differs from the other answer on the net.

If the OP would be so kind, as many of use can't unzip and read the file to get the answer posted above, can he copy the answer and post it directly on this forum, or even PM me?

[pakalikaPakalika]

I did the same thing as Richard_Benoit did, but the op said it was wrong to. This is the site I found.

http://wiki.xkcd.com/irc/Talk:Puzzles#Magic_Watch

Where I got my info from. BUt I want to see what the OP says.

[thisiskyle]

I did the same thing as Richard_Benoit did, but the op said it was wrong to. This is the site I found.

http://wiki.xkcd.com/irc/Talk:Puzzles#Magic_Watch

Where I got my info from. BUt I want to see what the OP says.

I haven't said any solutions were right or wrong. The only thing I said was wrong was that you could get two pieces of information at once. The second solution mentioned in the link above is exactly the same as the solution I posted (sorry if you couldn't open it). I'll put it here (I copied this from the link because this explanation was more concise than mine.):

Q1 - "If I ask you if behind door number 1 is a car, will you turn blue?"
Q2 - "If I ask you if behind door number 2 is a car, will you turn blue?"

If it turns blue on the first one, then the car is on door number 1.
If it turns blue on the second one, then the car is on door number 2.
If it turns [red] on both, the car is on door number 3.

I had originally "solved" it a different (lame) way that was sort of cheating and, therefore, discarded. Paul's post reminded me of it. It involved asking question to which there was no answer and taking advantage of the fact that the watch would, presumably, not light at all. This is just an assumption, however, as it was not mentioned in the description of the watch. I had thought that if I asked a question like
"If the prize is behind door number one, does one plus one equal two?"
which would (again, presumably) only light at all if the prize was behind door number one. This seemed like kind of a cop-out solution though...

[thisiskyle]

As far as I could tell.

If you ask the watch:

"is the prize behind either of these two doors?" (1 and 2) (you get a color doesn't matter which red or blue)

Then ask:

"is it behind either of these two doors?" (2 and 3) (you would get the same or opposite color you got from the first question)

At which point you should be able to figure it out. Granted we are allowed such questions.

Does that work or make sense?

This doesn't work.
If you list out all possibilities for the results of the two questions:
Assume red is yes and the prize is behind door...
...1 - RB
...2 - RR
...3 - BR
Assume blue is yes and the prize is behind door...
...1 - BR
...2 - BB
...3 - RB

So if you get RR or BB you know the prize is behind door 2 but if you get either RB or BR your left with a 50/50 between doors 1 and 3.

[Richard_BenoitEnglipedia Drone]

Ah ok! That hint was gigantic! I could ask a hypothetical question then. Like "If the prize is behind door number 1 will you shine blue?" Then if he shines red/blue I have trapped it into telling me two pieces of info?

But isn't your answer just a variation of what I said earlier?

[thisiskyle]

It is exactly what you said earlier but you didn't sound sure so I didn't want to say you were right if you were just starting to think along those lines and ruin it. Which is why I said I wasn't assigning a value judgement to it. When I said "no" I was answering "...have [I] trapped it into telling me two pieces of info?" and I stand by statement. I tried to make it clear that I was not saying you were on the right or wrong track but simply that the watch won't give you two pieces of info for the price of one. Apparently this was was not conveyed very well. I'm sorry if I thew you off; it was not my intent.

[Richard_BenoitEnglipedia Drone]

Ahhhhh ok! I read the "no" to be saying that I couldn't go down that route.