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Bufty
10-14-2006, 05:43 PM
Hi TR,

For putting us through that 4 letter verb thing. ;)

I encountered this nutmeg of a brain-stretcher over fifty years ago and I'm just hoping you haven't seen it before. It's not a trick question.

A Professor hands his student 12 metal balls. They look and feel identical but ONE of them does not weigh the same as the other eleven by an amount only detectable through the use of a balance-scale. The Professor wishes to know if the student can identify that particular ball in no more than three uses of the balance-scale and say whether it is heavier or lighter.

The student eventually discovers that using the balance-scale no more than THREE times, he can always identify which one out of twelve objects is different in weight and tell whether it is heavier or lighter than the others.

How?

THE SOLUTION IS IN POST 65 BELOW

writerterri
10-14-2006, 10:23 PM
Weigh 4 at a time seems like the logical way, right?

aadams73
10-14-2006, 10:34 PM
:e2zipped:

jbal
10-14-2006, 10:47 PM
Weigh 4 at a time seems like the logical way, right?
That doesn't tell you which specific one it is, plus it's a balance scale (something on both sides)

maestrowork
10-14-2006, 11:45 PM
Weigh 4 at a time seems like the logical way, right?

It's a good start.

Keep going... :) Think process of elimination...

Godfather
10-15-2006, 01:19 AM
1st go - weigh 1.
2nd go - weigh another.
3rd go - threaten to beat the teacher with the scales until he tells you.

clockwork
10-15-2006, 01:29 AM
Pishaw! This is so simple.

The man takes the chicken across first, leaving the fox and grain together on the other side. He returns and gets the fox, but when he deposits the fox on the other side, he takes the chicken BACK across, so that the fox and chicken aren't left alone together. He drops the chicken off back on the other side, picks up the grain, and takes it across to deposit with the fox.

Finally, he returns to retrieve the chicken and takes it to the other side.

Next.

dpaterso
10-15-2006, 01:54 AM
Nice one Bufty, I hadn't heard this before.

Not knowing whether the rogue ball is lighter or heavier than the others throws off my calculations every time. If I knew which, I'm pretty sure I could find the rogue in 3 uses of the scales. Without knowing, I'd be unsure which group of balls to dismiss when the scales don't balance.

Chris, get real, the freakin' fox is going to run away.

-Derek
My Web Page - naked women, bestial sex, and whopping big lies. (http://hometown.aol.co.uk/DPaterson57)
It's a helluva day at sea, Sir!

clockwork
10-15-2006, 02:03 AM
Chris, get real, the freakin' fox is going to run away.



Not if the farmer breaks its legs, it won't.




(What's a farmer doing with a fox anyway?
Yes, I had smart-a$$ for dinner)

aadams73
10-15-2006, 02:05 AM
What if it's a fox with no legs? S'not going too far then, is it? Not unless it rolls.

writerterri
10-15-2006, 02:09 AM
Oh, I know!

Weigh half and half- that's one

Then half and half of that- that's two

Then you're stuck with three and no more weigh in's.

Back to the drawing board...

Am I close though?

Bufty
10-15-2006, 02:12 AM
Sorry - you get no clues on this one from me. Keep trying - it's far more satisying when you do finally solve it.




Am I close though?

jbal
10-15-2006, 02:13 AM
Oh, I know!

Weigh half and half- that's one

Then half and half of that- that's two

Then you're stuck with three and no more weigh in's.

Back to the drawing board...

Am I close though?
No, because you don't know whether the odd one's heavier or lighter. If you balance six and six, one side will be heavier, but you still can't eliminate either group. I think I'm looking at this the wrong way too, but not sure how yet.
ETA: does anyone know if TR has even looked at this thread?

Bufty
10-15-2006, 02:16 AM
Yup, that had me stumped for hours, too, but it's a great feeling when you do finally solve it.

Rep me or PM me if you think you've got it.

Don't want TsukiRyoko let off the hook!! :snoopy:


Nice one Bufty, I hadn't heard this before.

Not knowing whether the rogue ball is lighter or heavier than the others throws off my calculations every time. If I knew which, I'm pretty sure I could find the rogue in 3 uses of the scales. Without knowing, I'd be unsure which group of balls to dismiss when the scales don't balance...
-Derek
My Web Page - naked women, bestial sex, and whopping big lies. (http://hometown.aol.co.uk/DPaterson57)
It's a helluva day at sea, Sir!

clockwork
10-15-2006, 02:17 AM
What if it's a fox with no legs? S'not going too far then, is it? Not unless it rolls.

A rolling fox is worth two in the bush.

I can make jokes because I do know how to do the scale riddle. ;)

aadams73
10-15-2006, 02:18 AM
A rolling fox is worth two in the bush.

I can make jokes because I do know how to do the scale riddle.

Ditto.

What about two rolling foxes in the bush?

writerterri
10-15-2006, 02:20 AM
I got it!


Weigh, 4, 4. That's one.

eliminate 4 and weigh 4 more. That's two

Then I have 2 and 2 left...shoot

clockwork
10-15-2006, 02:22 AM
Ditto.

What about two rolling foxes in the bush?

Two foxes rolling get their bushy tails tangled.

Bufty
10-15-2006, 02:23 AM
So you know you haven't solved it yet.

Stop fishing. :Hug2:

Rep or PM me if you think you've got it.


I got it!

Weigh, 4, 4. That's one.

eliminate 4 and weigh 4 more. That's two

Then I have 2 and 2 left...shoot

dpaterso
10-15-2006, 02:25 AM
Maybe it's a mutant swamp fox with no legs and he wants to sell it to one of those scientist fellers he seed on TV.

Well g'night all, I'm being summoned by She Who Must Be Worshipped, duty calls, wish me luck.

-Derek
My Web Page - naked women, bestial sex, and whopping big lies. (http://hometown.aol.co.uk/DPaterson57)
Daddy, I got cider in my ear.

writerterri
10-15-2006, 02:27 AM
http://smileys.smileycentral.com/cat/4/4_2_110.gif (http://www.smileycentral.com/?partner=ZSzeb001_ZSYYYYYYYYUS)





http://www.smileycentral.com/sig.jsp?pc=ZSzeb097&pp=ZSYYYYYYYYUS (http://smiley.smileycentral.com/download/index.jhtml?partner=ZSzeb097_ZSYYYYYYYYUS&utm_id=7925)

Bufty
10-15-2006, 02:42 AM
Sorry, Clock-work, you do not know how to do it. Your Repped solution was wrong and I've PM'd you to point out why.


A rolling fox is worth two in the bush.

I can make jokes because I do know how to do the scale riddle. ;)

clockwork
10-15-2006, 02:59 AM
Check again. :)

jbal
10-15-2006, 03:19 AM
So far, I can do it in four all day. Pretty sure I have step one just by the logic of eliminating as many as possible. My four step solution works in three depending on the outcome of step 2. I'm soooo close...

maestrowork
10-15-2006, 04:02 AM
I got it!


Weigh, 4, 4. That's one.

eliminate 4 and weigh 4 more. That's two

Then I have 2 and 2 left...shoot


You're on the right path, but not quite. I can't give you clues... :) But think "what's left..." ;) Also, it's not a one-two-three answer... the next steps depend on the results from the previous step... oops, I already said too much. Bufty is gonna kill me...

robeiae
10-15-2006, 04:20 AM
You can follow the same solution if you have 13 or 14 balls, too. :D

jbal
10-15-2006, 04:25 AM
Ok, I've got it to where I identify the ball, butdepending on the outcome of the third weighing I may not know whether it's lighter or heavier. This is hard.

maestrowork
10-15-2006, 04:35 AM
The not knowing whether it's lighter or heavier is the hard part. Otherwise, the answer is very simple. The "lighter/heavier?" part requires a different approach. But once you figure out the approach, it's really neat, because you will be able to figure out any number of balls.

writerterri
10-15-2006, 05:50 AM
The not knowing whether it's lighter or heavier is the hard part. Otherwise, the answer is very simple. The "lighter/heavier?" part requires a different approach. But once you figure out the approach, it's really neat, because you will be able to figure out any number of balls.


http://smileys.smileycentral.com/cat/36/36_6_6.gif (http://www.smileycentral.com/?partner=ZSzeb001_ZSYYYYYYYYUS)

My brain wont go there.






http://www.smileycentral.com/sig.jsp?pc=ZSzeb097&pp=ZSYYYYYYYYUS (http://smiley.smileycentral.com/download/index.jhtml?partner=ZSzeb097_ZSYYYYYYYYUS&utm_id=7925)

TsukiRyoko
10-15-2006, 06:08 AM
Damn, payback's a ***** indeed. :D OK, ok, I guess I had it coming.

hmm....

Is there a definate size to how big the balls are and how big the balance scale plates are? If no, then I would have to say you'd take 4 balls at a time and measure only 2 groups.

If they balanced out, then the lighter/heavieris in the unmeasured group, if they're unbalanced then you can identify which group the lighte/heavier ball is in.

Let's say the scale is unbalanced. Then, you split that group into 2, having 2 balls on each side (if it remains balanced, then just ditch the two groups and work with the unmeasrued group). Take a note of which side of the scale tips, then take a random balls, one from each side, and switch them. If the same side stays balanced, than the lighter/heavier ball was the one that wasn't moved. If the balaned tips to the other side, it was the ball that WAS moved.

Did I get it? If so, say thank you to homeschooling. :D

TsukiRyoko
10-15-2006, 06:09 AM
I like this method :D

maestrowork
10-15-2006, 08:10 AM
if it remains balanced, then just ditch the two groups and work with the unmeasrued group

then you just wasted one weighing. You won't be able to find the lighter/heavier ball with the remaining weighing.

TsukiRyoko
10-15-2006, 10:01 AM
Ah, true true..... Much more puzzling, but I'll be able to figure it out ;).

Bufty
10-15-2006, 01:58 PM
Then what do you think these are, Maestro? It's only simple to you because you know the answer. I assume you solved it with no help. Hint - with your super Mod -powers you could always delete posts that give clues. :Hug2:


I can't give you clues... oops, I already said too much. Bufty is gonna kill me...

Bufty
10-15-2006, 02:08 PM
:) Maestro - stop helping her - Pleeeeeeeese?

[quote=maestrowork].... Otherwise, the answer is....quote]

Bufty
10-15-2006, 02:46 PM
With thirteen or fourteen balls? You'll have to PM me your solution to prove that. Don't forget, the solution is infallible.


You can follow the same solution if you have 13 or 14 balls, too. :D

Spirit_Fire
10-15-2006, 03:28 PM
Ok, I think I've got it. I just posted my answer here, but I decided to cut it out and PM it to you! It's a secret!

Bufty
10-15-2006, 05:45 PM
Sorry, Spirit. Keep trying. :Hug2:


Ok, I think I've got it. I just posted my answer here, but I decided to cut it out and PM it to you! It's a secret!

Bufty
10-15-2006, 05:47 PM
Well done, Clock Work9. Fourth attempt, but you got it! Rep point on its way.

:partyguy:

Bufty
10-15-2006, 05:53 PM
Hope you're eyes and brain are going round in circles, Tsuki. Here's a clue - the answer's in the puzzle - work that one out, too! :roll:



Ah, true true..... Much more puzzling, but I'll be able to figure it out ;).

clockwork
10-15-2006, 05:59 PM
Well done, Clock Work9. Fourth attempt, but you got it! Rep point on it's way.

:partyguy:

Well, you know what they say. If at first you don't succeed, try, try again. And then try one last time.

Thank you for revealing the true nature of my hopelessly addictive personality to the aw community. ;)

Now. Back to the joking.

Tsuki. The answer is, the horse's name is Friday!

(you can do it, Tsuki!)

maestrowork
10-15-2006, 06:00 PM
:) Maestro - stop helping her - Pleeeeeeeese?


I've been officially flogged.

Bufty
10-15-2006, 06:06 PM
You masochistic devil -you. All the time it was only the pain you wanted.


I've been officially flogged.

maestrowork
10-15-2006, 06:20 PM
Bo Ron Ram... Bo Ron Ram...

PeeDee
10-15-2006, 06:26 PM
What is WRONG with you people!?

You do this kind of mental puzzle for FUN!?

Do you KNOW how much this has been bothering me for the past two days!?


AAGGGH!

*brain melts*

robeiae
10-15-2006, 06:32 PM
*brain melts*
*licks lips*

Can I get one of those with cheddar??

PeeDee
10-15-2006, 06:33 PM
It'll give you heartburn. It's the rapier wit which makes it so spicy.


:D

Bufty
10-15-2006, 06:34 PM
You claimed you could solve this with 13 or 14 balls.

I don't believe you. PM me and prove it.


*licks lips*

Can I get one of those with cheddar??

maestrowork
10-15-2006, 07:06 PM
The extra balls are for special man-handling...

maestrowork
10-15-2006, 07:13 PM
PeeDee and Clock are cheating!

clockwork
10-15-2006, 07:20 PM
PeeDee and Clock are cheating!

Hey! I worked it out legit and Pete doesn't give a sh*t so what's the harm, stinky-pink?

PeeDee
10-15-2006, 07:21 PM
PeeDee and Clock are cheating!

moy nayme ith Ray, an I'm a widdle whiner.

Sheesh.

clockwork
10-15-2006, 07:41 PM
moy nayme ith Ray, an I'm a widdle whiner.

Sheesh.

Let's get his lunch money and flush his head down the toilet.

Bufty
10-15-2006, 08:36 PM
Whether you solved it or not, I hope you had fun trying.

The solution is below in POST 65

jbal
10-15-2006, 08:37 PM
Whether you solved it or not, I hope you had fun trying.

http://www.absolutewrite.com/forums/showthread.php?t=22479
hey, no fair, I just pm'd you the solution! It's correct too.

ETA: wow, my solution is way more complicated than that. but it contains mathematical proofs and everything. It's three single spaced pages.

PeeDee
10-15-2006, 08:42 PM
Here's a riddle for those of you who aced the previous one. This one's trickier. Good luck!

Q: What did Deleware?














(answer: A brand New Jersey!)

clockwork
10-15-2006, 08:48 PM
Here's a riddle for those of you who aced the previous one. This one's trickier. Good luck!

Q: What did Deleware?

I dunno - Alaska.

Bufty
10-15-2006, 08:59 PM
Full credit to you, jbal. And yes, folks, I can confirm it was three pages!!

It may prove it mathematically, but I couldn't follow it!!

And if you've checked the solution and now know you were correct - hearty congratulations, friend.

AND TSUKIRYOKO- NO CHEATING!! YOU HAVE TO SWEAT IT OUT!!

ETA- I think you did well, Tsuki - see below.

Plus a well earned Rep point, jbal! You can now catch up on your sleep! :hooray:


hey, no fair, I just pm'd you the solution! It's correct too.

ETA: wow, my solution is way more complicated than that. but it contains mathematical proofs and everything. It's three single spaced pages.

TsukiRyoko
10-15-2006, 11:09 PM
OK, I'll be good and not check the solution link. It IS tempting though.... Give me a little bit, I'll get it. Nyeh heh heh ;)

TsukiRyoko
10-15-2006, 11:14 PM
Quick question- when you say "use the balance scale three times", can those turns be dissected down? Sat you have Turn 1,2 and 3. Is it allowed to split it into 1a, 1b, blah blah blah IF the balls are not all removed from the scale? Or am I pushing my luck?

dpaterso
10-15-2006, 11:52 PM
That so-called "solution" sounds mental, and I will not entertain it. A man must live or die by his convictions. This is such a time.

-Derek
My Web Page - naked women, bestial sex, and whopping big lies. (http://hometown.aol.co.uk/DPaterson57)
I once fought two days with an arrow through my testicle.

TsukiRyoko
10-16-2006, 12:23 AM
Okay, I think I really got it this time. And yes, I've been fair, no cheating or googling or anything. Well, I DID rip up 12 pieces of paper and test it out, but I don't think that counts as cheating.

OK here goes:

Split the balls in 4 groups, 3 balls in each. For the sake of making this is a little less complicated, let's label them groups 1111 2222 and 3333.

First, measure groups 1111 and 2222. Depending on the outcome, you'll measure them slightly differently. (This is where it gets kind of jumbled up, because there are a few different scenarios :rant: )

IF-it balances out, it means the mystery ball is in the 3333 group. If this happens, then you take only three balls out of each the 1111 group and the 3333 group. If the 111-333 group balances out, then you know that the unmeasured 3 ball is the mystery ball. If the mystery ball is the fourth, previously untouched ball, throw it onto the scale with a 1 ball on the other side. Then, you can tell if it is heavier or lighter. If the 111-333 does not balance out, then measure only two of the 3 balls. Depending on what you observed when you measured 111-333, youll know if the mystery ball is lighter or heavier, and youll know what to look for (if its heavier, one side will fall, etc) and if they balance out, once again it was the unmeasured ball.

Theres another scenario. Aye yahhh.

If the 1111 side falls or rises when measuring 1111-2222, then we know that we either have a light /heavy1 ball or a light/heavy 2 ball and all the 3s are normal. Now, we get to divide NEW groups (joy): 1113, 2221, and 3332. Throw 2221 and 3332 onto the scale. If they balance, mystery ball is in 1113 group. Should this happen, weigh two 1 balls. Like before, if they balance, the mystery ball is the unmeasured ball. If the 2221 side falls, then either the 1 ball is heavy or the 2 ball in 3332 is light. Now, weigh the 1 ball (from 2221) with a 3 ball. If they balance, the 2 ball was the mystery ball; if they dont balance, then the 1 ball was the mystery ball. Because 3 is the normal group, youll be able to tell if it was heavier or lighter.

*Pant, pant, pant * Ok, not quite done yet. Almost though, Bufty, almost. If the 2222 side happens to fall, then measure 1112 and 3331.(this leaves a 2223 group behind). Measure them roughly the same way we measured the balls in the last scenario (yes, Im now relying on your brains, because I dont feel like typing anymore or Im going to puke), making a few appropriate adjustments. Now, let me say: AHHHHHHHSDGHKDFGHFADGHFJKAGHF;AGHJKLF;AGHFJFJDFK;H AG;JSDFGHAFJKGH;F! I hope this is understandable. I can understand it, but I tend to get a little confusing when I'm explaining it, which is probably why this mile-long explanation just kind of crashes together.

And if I am wrong, I swear.... Oh ho ho ho ho, I swear.....

:D

Bufty
10-16-2006, 01:01 AM
Okay, Tsuki. Fair's fair. I'm going bananas trying to follow what you've written but I can tell from your method that you've probably got it.

But girl, when you see the simplicity of the solution you are going to kick yourself for struggling to write all that down like that.

And that's the point. The trying to write it down was your punishment!

Punishment served. Go check the solution. And here's a Rep point, and a hug. :Hug2:


Okay, I think I really got it this time. And yes, I've been fair, no cheating or googling or anything. Well, I DID rip up 12 pieces of paper and test it out, but I don't think that counts as cheating.

OK here goes:

Split the balls in 4 groups, 3 balls in each. For the sake of making this is a little less complicated, let's label them groups 1111 2222 and 3333.

First, measure groups 1111 and 2222. Depending on the outcome, you'll measure them slightly differently. (This is where it gets kind of jumbled up, because there are a few different scenarios :rant: )

IF-it balances out, it means the mystery ball is in the 3333 group. If this happens, then you take only three balls out of each the 1111 group and the 3333 group. If the 111-333 group balances out, then you know that the unmeasured 3 ball is the mystery ball. If the mystery ball is the fourth, previously untouched ball, throw it onto the scale with a 1 ball on the other side. Then, you can tell if it is heavier or lighter. If the 111-333 does not balance out, then measure only two of the 3 balls. Depending on what you observed when you measured 111-333, you’ll know if the mystery ball is lighter or heavier, and you’ll know what to look for (if it’s heavier, one side will fall, etc) and if they balance out, once again it was the unmeasured ball.

There’s another scenario. Aye yahhh.

If the 1111 side falls or rises when measuring 1111-2222, then we know that we either have a light /heavy1 ball or a light/heavy 2 ball and all the 3’s are normal. Now, we get to divide NEW groups (joy): 1113, 2221, and 3332. Throw 2221 and 3332 onto the scale. If they balance, mystery ball is in 1113 group. Should this happen, weigh two 1 balls. Like before, if they balance, the mystery ball is the unmeasured ball. If the 2221 side falls, then either the 1 ball is heavy or the 2 ball in 3332 is light. Now, weigh the 1 ball (from 2221) with a 3 ball. If they balance, the 2 ball was the mystery ball; if they don’t balance, then the 1 ball was the mystery ball. Because 3 is the normal group, you’ll be able to tell if it was heavier or lighter.

*Pant, pant, pant * Ok, not quite done yet. Almost though, Bufty, almost. If the 2222 side happens to fall, then measure 1112 and 3331.(this leaves a 2223 group behind). Measure them roughly the same way we measured the balls in the last scenario (yes, I’m not relying on your brains, because I don’t feel like typing anymore or I’m going to puke), making a few appropriate adjustments. Now, let me say: AHHHHHHHSDGHKDFGHFADGHFJKAGHF;AGHJKLF;AGHFJFJDFK;H AG;JSDFGHAFJKGH;F! I hope this is udnerstandable. I can understand it, but I tend to get a little confusing when I'm explaining it, which is probably why this mile-long explanation just kind of crashes together.

And if I am wrong, I swear.... Oh ho ho ho ho, I swear.....

:D

Rachael
10-16-2006, 08:23 AM
I looked at the answer and I still don't get it.

Whatever... I should find a good logic problem and post it.

Bufty
10-16-2006, 03:09 PM
SOLUTION TO TSUKIRYOKO PENITENCE PUZZLE


Congratulations to all who tackled this - I hope this solution is clearer than the earlier, now removed, explanation.

The key to this is in the second weighing.

Divide balls into three groups of 4 -- A(4) B(4) C(4)

First weigh A(4) and B(4)

Note whether the scale balances or whether it moves, and if it moves remember which group moved up or down and therefore could contain either a lighter or heavier ball.

For example - If A(4) goes down then the A(4) balls should be remembered as possibly containing a heavier ball. And if the B(4) balls go up, as they would in this case, the B(4) balls should be remembered as possibly containing a lighter ball. Or vice versa.

Then, for the second weigh, whether the first weighing balanced or not, introduce 3 unweighed balls from group C and shunt the balls (already on the scales) along so the scales then contain

C(3)A(1) and A(3)B(1)

The following are now your choices for the third and final weighing.

IF the scale balanced originally and STILL balances, the odd ball is the remaining C ball. Weigh it with any other ball and you know whether it is lighter or heavier.

IF the scale still moves IN THE SAME WAY as in the original balance, the odd ball is either A(1) or B(1) because they are the only balls still in their original position. You already know whether the A or B groups are heavier or lighter, so weigh either of A(1) or B(1) with any other ball and you have the answer.

IF the scale moves THE OPPOSITE WAY to the original balance, the odd ball is in A(3) because that is the only group you moved from one scale to the other. You already know whether group A was lighter or heavier, so weigh any two of A(3) and you have the answer.

IF the original 4x4 balanced and the scales are NOW UNBALANCED you know the odd ball is in group C(3) because they are the only new balls that you introduced. You also know whether C(3) contains a heavier or lighter ball. Weigh any two of C(3) and you have the answer.

IF the original 4x4 weighing did not balance, but NOW IT DOES BALANCE, the odd ball is in the group B(3) because they are the only balls that have been removed from the scale. You already know whether that group was lighter or heavier, so weigh any two of (B3) and you have the answer.

***************

dpaterso
10-16-2006, 05:50 PM
First weigh A(4) and B(4)

Note whether the scale balances or whether it moves, and if it moves remember which group contains the potentially heavier/lighter ball.

Sorry, can you dumb it down a little (please!!) and explain how you know which of these 2 groups contains the lighter/heavier ball?

If (for example) the scale goes DOWN on the left, is that because the oddball is on the left and is heavier, or is it because the oddball is on the right and is lighter?

Not a trick question!

Signed, "Puzzled"
My Web Page - sci-fi, fantasy, horror, cyborgs, AIs, dragons, vampyres. (http://hometown.aol.co.uk/DPaterson57)
I laugh in the face of danger. Then I hide until it goes away.

maestrowork
10-16-2006, 06:06 PM
I think Bufty meant "remember which way the scale moves" and "which balls belong to which groups." The rest of the logic depends on if the scale moves the SAME way or the other way. Also, you need to remember if the balls being weighed (or not) the second and third times belonged to A, B, or C -- meaning, don't mix them.

For example, in this case:

IF the scale still moves IN THE SAME WAY as in the original balance, the odd ball is either A(1) or B(1) because they are the only balls still in their original position. You already know whether the A or B groups are heavier or lighter, so weigh either of A(1) or B(1) with any other ball and you have the answer.

In order to get it right on the third weighing, you need to remember how the scale moves originally, and which one is A(1) and which is B(1):

1. If As were heavier than Bs, and now A(1) balances with a normal ball, that means B(1) is the odd ball and it's lighter
2. If As were heavier than Bs, and now A(1) is heavier than a normal ball, that means A(1) is the odd ball and it's heavier

Similar logic for As lighter than Bs...

Bufty
10-16-2006, 06:33 PM
That's exactly it. You've answered your own question. I've added a bit for clarification in the solution. Thanks for pointing out the area of doubt.

If A(4) goes down then the A(4) balls are earmarked as possibly containing a heavier ball. And if the B(4) balls go up, as they would in this case, the B(4) balls are earmarked as possibly containing a lighter ball.

Or vice versa.


Sorry, can you dumb it down a little (please!!) and explain how you know which of these 2 groups contains the lighter/heavier ball?

If (for example) the scale goes DOWN on the left, is that because the oddball is on the left and is heavier, or is it because the oddball is on the right and is lighter?

Not a trick question!

Signed, "Puzzled"
My Web Page - sci-fi, fantasy, horror, cyborgs, AIs, dragons, vampyres. (http://hometown.aol.co.uk/DPaterson57)
I laugh in the face of danger. Then I hide until it goes away.

clockwork
10-16-2006, 07:27 PM
Whatever... I should find a good logic problem and post it.

PeeDee loves riddles. He's got some really good ones you should ask about.

jbal
10-16-2006, 07:34 PM
SOLUTION TO TSUKIRYOKO PENITENCE PUZZLE


Congratulations to all who tackled this - I hope this solution is clearer than the earlier, now removed, explanation.

The key to this is in the second weighing.

Divide balls into three groups of 4 -- A(4) B(4) C(4)

First weigh A(4) and B(4)

Note whether the scale balances or whether it moves, and if it moves remember which group moved up or down and therefore could contain either a lighter or heavier ball.

For example - If A(4) goes down then the A(4) balls are earmarked as possibly containing a heavier ball. And if the B(4) balls go up, as they would in this case, the B(4) balls are earmarked as possibly containing a lighter ball. Or vice versa.

Then, for the second weigh, whether the first weighing balanced or not, introduce 3 unweighed balls from group C and shunt the balls (already on the scales) along so the scales then contain

C(3)A(1) and A(3)B(1)

The following are now your choices for the third and final weighing.

IF the scale balanced originally and STILL balances, the odd ball is the remaining C ball. Weigh it with any other ball and you know whether it is lighter or heavier.

IF the scale still moves IN THE SAME WAY as in the original balance, the odd ball is either A(1) or B(1) because they are the only balls still in their original position. You already know whether the A or B groups are heavier or lighter, so weigh either of A(1) or B(1) with any other ball and you have the answer.

IF the scale moves THE OPPOSITE WAY to the original balance, the odd ball is in A(3) because that is the only group you moved from one scale to the other. You already know whether group A was lighter or heavier, so weigh any two of A(3) and you have the answer.

IF the original 4x4 balanced and the scales are NOW UNBALANCED you know the odd ball is in group C(3) because they are the only new balls that you introduced. You also know whether C(3) contains a heavier or lighter ball. Weigh any two of C(3) and you have the answer.

IF the original 4x4 weighing did not balance, but NOW IT DOES BALANCE, the odd ball is in the group B(3) because they are the only balls that have been removed from the scale. You already know whether that group was lighter or heavier, so weigh any two of (B3) and you have the answer.
Thanks for clarifying. I was thinking about this last night and had become convinced that the solution as posted would not work. Now I see what you're getting at, and it's perfectly sound, and a bit more concise than mine, because step 2 remains the same. Mine is valid, though, and so I'm posting it. I suspect there are quite a few more solutions than this, but it won't be me that figures them out. Hope this doesn't make your head hurt:



solution:
(Note:balls eliminated as candidates will be referred to as X)
(also note: the steps must encompass all 24 possible solutions to be valid. each final outcome is checked here for validity.)
Step 1: balance four balls on each side of the scale. if one side is heavier, go on to step 2a, keeping in mind that either one of 1-4 is lighter than the other balls, or one of 5-8 is heavier than the others. If the two sides balance, skip to step 2b. (as of this step, 16 possible solutions have been eliminated, leaving only eight.)

Step 2a: (four balls have been eliminated. the four that were on the lighter side of the scale in step one will henceforth be numbered 1 through 4, and cannto be heavier than the other balls. the four from the heavier side will be numbered 5 through 8, and cannot be lighter than their brethren. 4 ballsX2 + 8 ballsX1=16 possible solutions eliminated in this step.)

Balance 1,5, and X against 3,4,and 6.
if they balance, go to step 3a
if 1,5,and X are heavier, go to step 3b
if 1,5,and X are lighter, go to step 3c

Step 3a: (balls # 1,5,3,4,6 have been eliminated, also eliminating five possible solutions. three remain. 2(L), 7(H) and 8(H) remain, with L and H as a reminder representing the lighter or heavier sides of step 1 respectively)

Balance 7 against 8.
if one side is heavier, that ball is the culprit, and is heavier than the other balls.
if they balance, ball #2 is lighter than the other balls.

(step 3a results in 3 possible solutions, added to 5 eliminated in step 2a and 16 in step 1. total:24 possible solutions).

Step 3b: (balls # 1,2,6,7,8 are eliminated by the outcome of step 2a. this eliminates five possible solutions. three remain.3(L), 4(L), 5(H))

Balance 3 and 5 against two Xs.
if Xs are heavier, #3 is lighter than the other balls.
if Xs are lighter, #5 is heavier than the other balls.
If XX=3,5, then #4 is lighter than the other balls.

(Step 3b results in three possible solutions, added to five eliminated in 2a, and 16 in step 1. total:24 possible)

Step 3c: (balls # 2,3,4,5,7,8 have been eliminated by the outcome of step 2a, eliminating six possible solutions. two remain. 1(L) and 6(H).

Balance #1 against X.
if they balance, then #6 is heavier than the other balls.
if X is heavier, then #1 is lighter than the other balls.

(step 3c includes 2 possible solutions, added to six eliminated by step 2as outcome, and 16 eliminated by step 1. Total:24.)



Step 2b: (8 balls and thus 16 solutions have been eliminated by the outcome of step 1. 4 balls remain, and each could be heavier or lighter than the others, leaving 8 possible solutions. Remaining balls will be henceforth be numbered as 9 through 12.)

Balance #9,10 against #11,X.
if it balances, go to step 3d
if 9,10 is heavier, go to step 3e
if 9,10 is lighter, go to step 3f

Step 3d: (balls # 9,10, and 11 have been eliminated along with six possible solutions. only #12 remains.)

Balance #12 against X
ball # 12 is the culprit and will be heavier or lighter than X. 2 possible solutions+6 from step 2b+16 from step 1 = 24.)

Step 3e: (ball # 12 has been eliminated along with 3 other solutions [these are 11(H), 9(L), 10(L)], for a total of 5 solutions eliminated by the outcome of step 2b.)

Balance #9 against #10.
if #9 is heavier, it is heavier than the other balls.
if #10 is heavier, it is heavier than the other balls.
if the scale is balanced, then #11 is lighter than the other balls.

(3 solutions in this step+5 eliminated by step 2b+16 solutions by step 1=24 solutions.)

Step 3f: (ball#12 is eliminated along with three other solutions [11(L), 9(H), 10(H)] for a total of 5 solutions eliminated by the outcome of step 2b.)

Balance #9 against #10.
if #9 is heavier, #10 is lighter than the other balls.
if #10 is heavier, then #9 is lighter than the others.
if they balance, #11 is heavier than the others.

(Step 3f encompasses 3 solutions+5 from step 2b+16 from step 1=24 solutions.)





As additional proof, each of the 24 possible solutions should be represented in one of these six versions of step 3. note that the nomenclature of step 1 can be reversed, so that opposite solutions for the first 8 balls can be deduced in the same manner, thus the 8 n/as appearing below. To repeat: These solutions are encompassed by the same steps as their counterparts by a reverse of the nomenclature. This chart lists where each possible outcome occurs in one and only one version of step 3:
1(L)=3c
1(H)=n/a
2(L)=3a
2(H)=n/a
3(L)=3b
3(H)=n/a
4(L)=3b
4(H)=n/a
5(L)=n/a
5(H)=3b
6(L)=n/a
6(H)=3c
7(L)=n/a
7(H)=3a
8(L)=n/a
8(H)=3a
9(L)=3f
9(H)=3e
10(L)=3f
10(H)=3e
11(L)=3e
11(H)=3f
12(L)=3d
12(H)=3d

PeeDee
10-16-2006, 08:09 PM
PeeDee loves riddles. He's got some really good ones you should ask about.

You come near me with one of those riddles, I'll break your kneecaps and throw you in the river.

THis is just a general warning.

(with this ball riddle, I had to have it explained to me like I was autistic. Someone sitting there going "This ball is heav-y. Heavy-ER than THOSE balls, mmkasy? Good peedy!")

Bufty
10-16-2006, 08:23 PM
I would think it was yours that would be hurting, jb. Cripes, I thought I had a corkscrew mind. Give the puzzle to your mates and hand them that as the solution - then run!

You deserve a medal, friend. :)


..... Hope this doesn't make your head hurt:

PeeDee
10-16-2006, 08:25 PM
Give 'em the solution at the same time as the puzzle. It'll STILL take hours to figure out....!

*stomps off*

Angelinity
10-16-2006, 09:10 PM
yeah! some of us hurt ourselves knocking this around.

time for a bufty pennitence...

any hands? :hi:

Bufty
10-16-2006, 10:19 PM
Whoa! Don't blame me because your brain cells went on strike. :poke:


yeah! some of us hurt ourselves knocking this around.

time for a bufty pennitence...

any hands? :hi:

jbal
10-16-2006, 10:20 PM
yeah! some of us hurt ourselves knocking this around.

time for a bufty pennitence...

any hands? :hi:
I disagree. See, Bufty's puzzle had a solution...

Bufty
10-16-2006, 10:32 PM
Yep - that's probably what some folk hurt themselves on! :roll:
Ooooops, I'm maybe pushing my luck...


I disagree. See, Bufty's puzzle had a solution...

Angelinity
10-16-2006, 10:35 PM
Whoa! Don't blame me because your brain cells went on strike. :poke:

LOL! i've been dreaming of twelve balls on a balance beam :D

clockwork
10-16-2006, 10:37 PM
You come near me with one of those riddles, I'll break your kneecaps and throw you in the river.

THis is just a general warning.

(with this ball riddle, I had to have it explained to me like I was autistic. Someone sitting there going "This ball is heav-y. Heavy-ER than THOSE balls, mmkasy? Good peedy!")

:ROFL:

Tell 'em the one about the truck. That was such a good one...

Angelinity
10-16-2006, 10:37 PM
Yep - that's probably what some folk hurt themselves on! :roll:
Ooooops, I'm maybe pushing my luck...

hmm... at least you got a good laugh?

writerterri
10-17-2006, 01:20 AM
My brain deflated after the second weigh in. :Shrug:

PeeDee
10-17-2006, 02:25 AM
:ROFL:

Tell 'em the one about the truck. That was such a good one...

You people think I don't have a baseball bat within easy reach, but you're wrong. Oh boy oh BOY are you sooooo wrong.

*stomps off to make tea*

clockwork
10-17-2006, 02:58 AM
Fine. Be like that. I'll post a new riddle instead.

If Pete is locked in a windowless room with a copy of "Puzzles! Puzzles! Puzzles!" and given three hours to solve the lot, how much more annoyed is he?

:D

aadams73
10-17-2006, 03:03 AM
The answer is...sh!tloads!!

PeeDee
10-17-2006, 03:05 AM
Fine. Be like that. I'll post a new riddle instead.

If Pete is locked in a windowless room with a copy of "Puzzles! Puzzles! Puzzles!" and given three hours to solve the lot, how much more annoyed is he?

:D

Depends on how long it takes him to eat the pages.

clockwork
10-17-2006, 03:12 AM
Depends on how long it takes him to eat the pages.

http://i63.photobucket.com/albums/h134/clockwork9/papers-1.jpg

Want some ketchup?

PeeDee
10-17-2006, 03:16 AM
On second thought, maybe I'll use mucus from the back of my throat to dress myself completely in those pages. And then I'll dance around the room singing Milli Vanilli songs.

clockwork
10-17-2006, 03:24 AM
On second thought, maybe I'll use mucus from the back of my throat to dress myself completely in those pages. And then I'll dance around the room singing Milli Vanilli songs.

:ROFL:

I thought you were going to talk about that guy in the X-files for a second there. I did that myself a couple of weeks ago. There were a stack of old newspapers in the office and there was a bit of a dumb debate about exactly what to do with them. Various wise-cracks ensued but I kind of killed the mood with - I'll throw up a load of bile and mucus and then build a nest to inhabit between murders like that Tooms guy in the X-Files.

Nobody at work gets my humour. And by 'my humour' I mean anything that is even just a splinter off from the mainstream of catchphrase-quoting/I got so drunk/you're so gay banality that everyone else seems so happy with. :cry:

PeeDee
10-17-2006, 03:29 AM
Tooms! THAT was his name. Good thing you said it, or it was going to bother me...

That guy was friggin' spooky. Not as bad as the inbred sons and their inbred mother who they kept underneath their bed. That was terrifying.

clockwork
10-17-2006, 03:34 AM
I just got Season 1 of The X-Files recently. Squeeze and Tooms are truly creepy episodes but some of the others are sooooo dated. Scully's hair is an X-File of its own and episodes I used to love don't do it for me anymore. Darkness Falls (the one with the little green bacteria that eat people at night) used to be terrifying - but watching it again... not so much.

Good at the time though. :)

PeeDee
10-17-2006, 03:40 AM
My wife and I are watching them now and then. We're up through most of season four now, which is when it really starts taking off. "Confessions of a Smoking Man" is my favorite episode ever. Brilliant writing.

We also just re-watched Millennium, also by Chris Carter, which really should have lasted more than a few seasons. That was such a cool show.

We also have "The Lone Gunman" series that spun-off the X-Files. That one's notsomuch.

clockwork
10-17-2006, 03:47 AM
Yeah, Confessions is great. Can't claim to have seen them all I'm afriad but I remember loving the the three that made up Gethsemane, Redux and Redux II. Lots of twisties.

TsukiRyoko
10-18-2006, 06:42 AM
Ha, it was fun. yeah, you did get me. Writing all that sucked, but I like brain teasers. ;)


-I just checked the solution. I decided it was only fair to myself to bring my foot up above my head and kick myself in the face. The answer was barely a third of mine! :P

TsukiRyoko
10-18-2006, 07:53 AM
On second thought, maybe I'll use mucus from the back of my throat to dress myself completely in those pages How did YOU figure out West Virginia's secret to paint houses?

aadams73
10-18-2006, 01:11 PM
I just got Season 1 of The X-Files recently.

X-Files was really fantastic. Scully's hair and shoulderpads though...*shiver*

Rachael
10-19-2006, 02:49 AM
Give 'em the solution at the same time as the puzzle. It'll STILL take hours to figure out....!

*stomps off*

Lol, no kidding...

Soccer Mom
10-19-2006, 03:20 AM
Oh, I love the X-files with the bugs in the woods that suck the people dry! But she does look so puffy and obviously pregnant in that one. Tooms is a classic.

Mulder with bile dripping off of his finger: How can I get this off without betraying my cool exterior. :D

aadams73
10-19-2006, 03:26 AM
The X-files episode with the roaches really freaks me out. I think my favorite episode is "Home."

Soccer Mom
10-19-2006, 03:29 AM
What's the one with the lake monster? I love that one. I think the creature ones are my favorites.

aadams73
10-19-2006, 03:35 AM
Oh yeah, doesn't Scully's dog get eaten or something?