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Puzzle of this year :)

 
lydia westland
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This is the most difficult puzzle I've ever met. I was so excited when I made it that I couldn't fall in sleep that night.
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12 balls, look exactly the same. only one of the twelve balls is not standard; the other 11 is of the same weight. but you don't know whether it's heavier or lighter. With a scale, how can you identify which ball is not standard in three times? (you know which side of the scale is lighter or heavier when the balance is not maintained)
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have fun :roll:
 
Cindy Glass
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OK - how about:

Put 6 on each side. Take the 6 from the heavier side (lower side) and set them apart.
Take the lighter 6 and put 3 on each side. Take the 3 from the heavier side (lower side) and set them apart.
Take the last 3 and put one on each side and one left off.
- If the scales balance then the one you left off is the light ball.
- If the scales do not balance then take the one from the higher side and it is the lightest.


[ May 06, 2002: Message edited by: Cindy Glass ]
 
Corey McGlone
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I'm not so sure that works, Cindy. According to the original question, you don't know if you're looking for a ball that's lighter or heavier - it's just different.
Therefore, if you first put 6 on either side, one side will be heavier than the other but, if the irregualr one is lighter, it'll be in the light side but, if the irregular ball is heavier, it'll be on the heavier side. Therefore, you can't simply eliminate the heavy 6 because the irregular ball might very well be among them.
Corey
 
Cindy Glass
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Ah yes - well that makes it more difficult.
Well I can get it done in 4 weighings. . .
 
Cindy Glass
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OK - how about:

Pick 6, put 3 on each side. If they are the same then the different ball is not in this batch at all. If they are NOT the same then the different ball is one of these 6. Either way you know which 6 it is in. Set the other balls aside.
Pick out 3 of the ones containing the different one, put on one balance. Put 3 of the ones that you set aside on the other side (these 3 you know are the same). If they balance then the different one is one of the last 3. If they don't balance then the different one is one of the 3 you picked from the different ones. You can also tell if the 3 containing the different one is lighter or heavier than the 3 "control" balls.
Using these 3 containing the different one, pick two and weigh them. If they balance, then the remaining one is the different one. If the do NOT balance then the different one is either the lighter or the heavier depending on the results of the second weighing.

[ May 06, 2002: Message edited by: Cindy Glass ]
 
lydia westland
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Cindy,
That may not work either. For the last operation, you have three balls, and try to get the bad ball with the scale once. you cann't make it. If the scale is balanced, you win. how about the scale is not balanced? you do NOT know if the bad ball is lighter or heavier.
 
Johnson Chong
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How about you telling me the solution, I just say it's right or wrong base on emotional loves, without having to use my head.
After reading this, think....nothing. Or keep playing the song "Strange Love" continuously in your head. Or go sit in a lotus position, pre-empt your mind of all thoughts, mediate until you're one with the universe. If you choose not to do any of these, you don't know what you're missing.
[ May 06, 2002: Message edited by: Johnson Chong ]
[ May 06, 2002: Message edited by: Johnson Chong ]
[ May 06, 2002: Message edited by: Johnson Chong ]
 
Cindy Glass
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Yeah - there is a hole in that logic. But I don't have time to work it through today - maybe tomorrow.
 
Mark Spritzler
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How about.
Take 6 balls put 3 on each side, if they are the same, take the other 6 balls. If they are not use those 6.
Now Take 4 of the six balls, and put 2 on each side of the scales. If they equal, then you have the other 2 balls, where one is different. Otherwise, use the 4 balls.
Then I am not sure after that, but it is almost there. I think.
Mark.
 
Raul Sandoval
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I think I know the solution.
1. Put four balls on each side to find the
set where the odd ball is.
2. Put three balls from the odd ball set against
any three balls from the equal set.
3. If they balance, then the odd ball is the
remaining ball from the odd ball set.
4. If they don't, then you can now deduce
that the odd ball is heavier or lighter.
5. Put one ball against another ball in the
odd ball set.
6. If they balance, then the remaining ball is
your odd ball.
7. If they don't, the odd ball is the one
that is heavier if from #4 is heavier
or that is lighter if from #4 is lighter.
 
Cindy Glass
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Step one fails. If the balls on the scale (4 on each side) do NOT balance - Which set is the odd set?
 
Mark Spritzler
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Step one fails. If the balls on the scale (4 on each side) do NOT balance - Which set is the odd set?

You get him Cindy. After all his first post ever in JavaRanch and he answers the puzzle of the year.
Mark
 
Cindy Glass
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Yeah - well considering that I have not come up with the answer - he shouldn't feel too bad.
Of course my excuse is that I am WAY to busy at work to think about trivial puzzles :roll: .
 
Thomas Paul
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I think I got it:

1)Weigh 4 balls against 4 balls. If they balance, mark these as normal. Put a big "N" in magic marker on them. If they don't balance, then put an "H" on the balls in the side that went down, "L" on the balls in the side that went up, and "N" on the balls that are left.
2) Assuming they didn't balance. We have 4 balls marked "H", 4 balls marked "L" and 4 balls marked "N". Take one H, one L, and one N and weight them against two L and one H.
3a) If the side that has the 2-L goes up, then either one of the 2-L or the H from the other side is the odd ball. Weigh the two L against each other. The side that goes up is the odd ball. If neither goes up, it's the H that is the odd ball.
3b) If the side with the 2-L goes down, then the odd ball is either the H from that side or the H from the other side. Weigh the H against the other H. The side that goes down is the odd ball.
3c) If they balance, then the odd ball is either the other L or one of the remaining two H. Weigh one H against the other. The side that goes down is the odd ball. If neither side goes down, then the odd ball is the L.
Back to:
1) Assuming the first measure did balance, then we have 8 balls marked "N" and 4 balls without any mark.
2) Take 3 unmarked balls and weigh them against 3 balls marked N. If they balance, mark the unmarked balls with an "N". If the unmarked balls go down, mark them all with an "H". If the unmarked balls go up, mark them with an "L".
3a) If the second measure balanced, we have one unmarked ball which is the odd ball. Weigh it against any other ball to see if it is heavier or lighter.
3b) If the measure didn't balance, we now know
whether the odd ball is heavier or lighter and which of the three balls it is. Take two of the balls and weigh them against each other. If they balance, the remaining ball is the odd one. If they don't balance, then one of them is the odd ball. If the balls are marked L then it is the higher one. If the balls are marked H, it is the lower one.
And I think that covers every possibility.

[ May 07, 2002: Message edited by: Thomas Paul ]
 
Jim Yingst
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Good job, Thomas!
 
David Weitzman
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I heard this puzzle a few years ago from a tour guide in Israel. It took two days for me to work it out. I'm not sure I've ever seen another one quite as nice. No subtle tricks. No tricky language. Just pure mind-twisting experience.
 
Jim Yingst
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Yeah, same for me - the puzzle's been floating around for a while; I'm pretty sure it's even been posted in MD in the distant past, long deleted. I heard it years ago, and remember staying up very late one night until I worked it out. It's a very good challenge.
 
Thomas Paul
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I realized I was getting nowhere with it so I decided to work from the back end. What would I need to know in order to solve it when I'm down to 3 balls? I made the wrong assumption that I had to know by then whether the odd ball was heavier or lighter. I spent a long time chasing the wrong answer because of that wrong assumption. Once I realized my mistake it actually didn't take that long to solve the puzzle.
 
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