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Wed 10 Dec, 2003 01:45 pm
The last of my series of riddles...Hope you all had fun!
Placed in front of you is a "Lazy Suzan" with four shot glasses placed equally apart around the outer edge. They have been randomly placed either right side up or upside down and it is your challenge to get them all oriented the same way; that is, either all four up, or all four down, as quickly as possible.
Of course you will be blindfolded! You're not surprised...
Each turn the Lazy Suzan will be spun and you may then touch any two glasses, and then decide to keep each as it is or turn either one, or both, over. OK?
You may keep both that you touch the same, turn them both over, or turn just one of them over (your choice, either one). Obviously, as you reach down to grab two of the glasses you will be able to tell which two of the four you are touching - both in front of you; both away from you; the two on the left; the two on the right; or either of the two corner to corners.
You will start with a $10,000 Prize Fund which will be decreased by $1,000 after each turn. I will stand next to you and announce after each of your efforts as to whether or not you have solved the puzzle. Of course, there's no chance in the whole world that you will be so lucky as to start with all four in a winning position, but of course you already knew that. And also, if you decide to rely on luck to get you to the final solution you should understand that once the $10,000 Prize fund is gone, you will then have to start paying $1,000 for each wrong guess you make from then on out - No Stopping until you get it right!
Question: What process can you use to guarantee success?
Um...with shot glasses, you should be able to tell quite easily which side is up and which is down. Is the thing supposed to be indecipherable, as to which is up and which is down? I'm assuming yes, because otherwise there wouldn't be too much of a riddle.
you spin the 4 each time, so you know which ones are up, but not where they are. and you can only touch 2 each time.
bookmarking...?
How about this?
If they cannot start out all the same then they must be 2/2 or 3/1.
On your first attempt you check two adjacent glasses.If they are both the same you turn them both over. This has a 50/50 chance of ending it there and then, because if the split is 2/2 turning any two the same will result in all being the same. If the split is 3/1 you will not have made it any worse but you will now know which is in the majority. If they are different, then turn one of them over, say making them both upright. This will either solve the puzzle, change a 2/2 to a 3/1 or vice versa.
Second try you check two opposite glasses. One of these must be a glass you have already checked and one is not. If they are the same, leave them as they are. This tells you that there are now three the same and which way up they are. If they are different, turn the one that is different from how you left the first two. Either you have now won or there is one odd glass and you know which way to turn it.
There is an even chance of finding that glass next time, a three-in-four chance of finding it the next two times, so you would be extremely unlucky to leave with less than $5,000
Bookmarking is a method of getting this thread on to my list of threads watched. That way I am assured of seeing all postings in it without having to check a bunch of stuff.
Gotta "guarantee success" according to the puzzle, Mungo.
Mungo
You could still be there all day trying to find that last glass.
Hmmm. unecessarily complicated. Try again.
First attempt, check two adjacent glasses. If they are the same turn both over. This will either leave all four the same or a 3/1 split with the majority now being the way you left those two.
If different, turn either one of them over.
This will either result in all four being the same, or a 3/1 split with the majority being the way up that you leave the first two, or a 2/2 split.
Second attempt, check two opposite glasses. One of these must be one of those already checked and one not. Either they are the same or different. If the same, leave them. You now know for sure you have a 3/1 split and that the majority are the same way up as the way you left both first and second attempts.
If different, turn over the one that is not the same as the way you left the first two. Either this leaves all four the same way up or you know that you have a 3/1 split and that the majority are the same way up as the way you left the first and second attempt.
Either way, you have a 3/1 split, you know which way up the odd one is, and you have even chances of finding it next attempt.
Guarantee, huh? I guess that makes me the dummy around here again. So what's new?
All the same, odds of 127/128 that I will finish up with at least $1000 winnings is fine with me.
I'm still working on it.
Maybe 127/128 is the best that can be had -- but I've been doing puzzles like this for a very long time -- and even when they seem impossible, they usually have an answer that satisfies the "guarantee" requirement.
Question, Tet:
Must you touch the two glass simultaneously -- or may you touch one and then decide if you are going to make the other touch to the left, right, or across?
I'm hoping the latter, because if so, I think I have the solution.
Tet, forget that last question of mine.
I think I have the solution.
I'm sending it to you by PM.
By the way -- this was a great puzzle.
I ended up solving it by actually using shot glasses.
Damn, I wanna pat myself on the back -- because this one was tough.
The latter =P
You can touch any two glasses, but they don't need to be touched at the same time. So long as you only touch 2.
Can someone tell me how to send a message by PM? Please and thank you
P.M's figured out and one sent to Tetsuo with my version of the solution.
And 'yup', the solution is guaranteed just as you all said it had to be.
BTW Franki, how many 'choices' did you do it in? (I bet it's going to be less than my five! Grrrr!)
Five seems to be the minimum to guarantee a win, Mungo.
Go ahead and post your answers, both were great =P
First time out -- touch two corners. If they are both up or both down -- turn 'em over. You may get lucky. If the other two are the same, you've won. If the other two are different, you will not have won -- but you will know that three glasses are now facing in the same direction.
If the first touch comes up not being the same, turn one over and that will win if the two not being touched are both in that direction -- or leave you with three facing the same direction.
Either way -- after the first spin -- you will have three glasses facing the same direction.
(For ease in explaining the rest of the moves -- let us assume that there now are three facing up and one facing down.)
After the second spin -- touch any two adjacent glasses. If they are the different -- turn the one facing down, up -- and you will have won. If they are the same -- turn one over -- either one.
At that point, you will have two facing up and two facing down.
After the next spin -- touch two corners. If they are the same, turn both over and you've won.
If they are different -- leave them be -- and spin again.
After the spin -- touch any two adjacent glasses. If they are the same -- turn 'em over and you win.
If they are different, turn them over anyway. This will result in a sure thing next spin, because the two same facing glasses will be opposite each other on the corners.
Simply turn two corners over and you've won.
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