Ah-sweet mystery of life at last I found you!

[Poboy kartman]

nice idea..
but no.
it's easier than that.. even if I glue some of the coins to the table,
so that you cannot even move them.. let's say three

'sid

Funny you should say that- 3 is an important part of another coin puzzle. At least when you have 8 unbalanced coins. Oh and one more clue think "outside of the box". (They go together).

 

[itsid]

Okay.. here we go.. the letter.

A
AA
BA
ABAA
AAABBA
CABBAA
ACAABBBA
AAACBACBAA
the next line is:
CAACABAAACABBA
Why? let's convert to numbers..
the puzzle starts with
1
11 (one one in the line before)
21 (two ones in the line before)
1211... (one two and one one in the line before)

every line describes the line above
so when you come down to

111 3 2 1 3 2 11
the next line is:
31 13 12 11 13 12 21

and you can go on for as long as you like, you'll never hit a 4 (or a D)


As a hint for the coins..:
try it without the blindfold,
pick any six coins from a group of 12 (6 face up, 6 down)

And if you look at the coins, you'll notice.
(that's how I solved the puzzle)

'sid

 

[OzFab]

That's quite clever, I even had to read it twice before I got it...

 

[Poboy kartman]

Okay.. here we go.. the letter.

A
AA
BA
ABAA
AAABBA
CABBAA
ACAABBBA
AAACBACBAA
the next line is:
CAACABAAACABBA
Why? let's convert to numbers.. p
the puzzle starts with
1
11 (one one in the line before)
21 (two ones in the line before)
1211... (one two and one one in the line before)

every line describes the line above
so when you come down to

111 3 2 1 3 2 11
the next line is:
31 13 12 11 13 12 21

and you can go on for as long as you like, you'll never hit a 4 (or a D)


As a hint for the coins..:
try it without the blindfold,
pick any six coins from a group of 12 (6 face up, 6 down)

And if you look at the coins, you'll notice.
(that's how I solved the puzzle)

'sid

No you lost me on the coins. I see two groups with different numbers. Please to explain. ..me so confused.

 

[Poboy kartman]

BTW- I didn't mean for the 12 coin/ balance scale to be a mystery for the ages- so unless someone objects, I will reveal the answer tomorrow evening.

 

[itsid]

No you lost me on the coins. I see two groups with different numbers. Please to explain. ..me so confused.

yes, exactly.. but what are the numbers you see??

'sid

 

[Poboy kartman]

yes, exactly.. but what are the numbers you see??

'sid

Ah- I believe I see it now- but if it's what I think. Isn't that more than two groups open to interpretation and only able to be verified (or even selected) without a blindfold?

 

[itsid]

Ah- I believe I see it now- but if it's what I think. Isn't that more than two groups open to interpretation and only able to be verified (or even selected) without a blindfold?

I think you don't see it yet

'sid

 

[Poboy kartman]

OK- I've already explained the procedure for 8 balanced coins, so I'm just going to explain what to do when 4 on each side don't balance. For simplicity's sake, I'm just going to say heavy and light.

Take the top 3 coins off the heavy side and put them in front of the scale on the heavy side. Take the top 3 coins off the light side and put them on top of the last coin on the heavy side of the scale. Take 3 of the 4 coins that weren't weighed or take them "out of the box" lol. Put them on top of the last coin on the light side.

Scenario#1: The scale stays the same. You have eliminated everything but the bottom 2 coins. Put everything else in a pile and put the light coin in front of the scale and replace it with another coin.

If the scale stays the same, the coin on the heavy side is a heavy counterfeit. If the scale balances it's the light counterfeit in front of the scale.

Scenario#2- The scale balances. You have eliminated everything but the 3 coins in front of the scale. Take everything else and put it in a pile. Put one coin in front of the scale and one on each side. If the scale balances the heavy counterfeit is in front of the scale. If it doesn't the side that goes down is a heavy counterfeit.

Scenario #3: The heavy side of the scale now becomes the light side. You have eliminated everything but the 3 top coins on what is now the light side. Put everything else in a pile and one in front and one on each side. If the scale balances the light counterfeit is in front of the scale. If not, the side that goes up is the light counterfeit.

This is only one solution, but it's the simplest and easiest to explain. One question I never got an answer to was how many different ways that there are to solve this puzzle.

Now that the easy one is out of the way, and your "out of the box" thinking has been primed.....

You're trying to solve the exact same problem at a bar. Your helpful drunk buddy puts 5 coins on each side of the scale. You can't change that so you only have 2 moves left.........

This is a pretty simple solution as well. No turning over of coins or anything. (That might come up later)........

 

[itsid]

....
Take the top 3 coins off the light side and put them on top of the last coin on the heavy side of the scale...

I am dissapointed..!!

I was hoping for a 'marking' free solution.

And all you do is instead of marking the coins is "ordering" the coins
"A vs B" or in your nomenclature "heavy vs light"

The exact same method (ordering) could be used in my solution as well.
Both of us need to individually track the B coin in the A stack
(light coin in heavy stack)..

As far as I'm concerned that's the same violation of rules

My understanding of the "do not mark" rule was:
if you have any number of coins on one side of the scale you are NOT ABLE TO TELL THEM APART, that is you do not know where they were before.

So, yeah.. NO!

'sid

 

[Poboy kartman]

I am dissapointed..!!

I was hoping for a 'marking' free solution.

And all you do is instead of marking the coins is "ordering" the coins
"A vs B" or in your nomenclature "heavy vs light"

The exact same method (ordering) could be used in my solution as well.
Both of us need to individually track the B coin in the A stack
(light coin in heavy stack)..

As far as I'm concerned that's the same violation of rules

My understanding of the "do not mark" rule was:
if you have any number of coins on one side of the scale you are NOT ABLE TO TELL THEM APART, that is you do not know where they were before.

So, yeah.. NO!

'sid

I think you need to re-read that post. I know where every coin was or is and the "heavy/light" only describes the position of the scale. For instance- there were 4 coins on the "heavy" (down) side of the scale. I took 3 off and put them in front of the scale. Without marking them (or even labeling them- "A or B" I know where they came from. I don't even have to remember because I put them in front of the scale on the down side. I left one on the scale. I moved 3 from the up side to the down- again I know the top 3 coins came from the up or "lighter" side of the scale without marking, flipping, or calling them A or B. I also know that the bottom coin on that side hasn't moved. So I know where all those were and are now. I know that the 3 coins on top of the up side or "light" side of the scale came from the leftover pile of the only 4 coins know to be genuine at that point. Again, without flipping or designating those coins A or B , I know where they came from and where they are. I don't have to track every coin. The solution is there and it is simple.

It doesn't violate any of the rules of the parameters of the puzzle except in the most outlandish way- because technically I said only a scale and balance but I also used my brain.

Edit: How else could I describe it??????..

 

[itsid]

I think you need to re-read that post. I know where every coin was or is and the "heavy/light" only describes the position of the scale. For instance- there were 4 coins on the "heavy" (down) side of the scale. I took 3 off and put them in front of the scale. Without marking them (or even labeling them- "A or B" I know where they came from. I don't even have to remember because I put them in front of the scale on the down side.

I agree!

I left one on the scale. I moved 3 from the up side to the down- again I know the top 3 coins came from the up or "lighter" side of the scale without marking, flipping, or calling them A or B. I also know that the bottom coin on that side hasn't moved.

That's what I'm talking about, stacking the coins in a specific order (former heavy coin lowest, three former light on top)
That's the exact same 'cheat' I did
I now KNOW that it is impossible to fullfill the task without cheating (marking, flipping or stacking)
And yes, I could also say leftmost and rightmost coin, doesn't make any difference.
Still I consider this as being a marked coin!
Why?
Because you track individual coins, not a group of four, but a single coin in a pile of four.
HOW you do it doesn't matter leftmost, bottom most, face down, painted pink, radioactive marker... all the same cheat.

truely unmarked coins would be:
you have two pouches in which you put the coins to balance, knot them, hand the pouches over, I give them a good shake, you balance them.

It doesn't violate any of the rules of the parameters of the puzzle except in the most outlandish way- because technically I said only a scale and balance but I also used my brain.

You violated your own rule;
you tracked an individual coin (the same as marking it)
you had to, since the puzzle is unsolvable for this situation (2 weighings, 8 coins, 1 counterfeit not known if heavier or lighter)
You need ONE more information to solve.

'sid

 

[Poboy kartman]

BTW- Sid,

A couple of things : I never said you couldn't describe the coins as A or B, just that I was getting confused and I thought you could describe the solution so it could be better understood by describing their locations and movements rather than labeling. I reposted your original solution in that manner as an example. You thought it was easier to understand your way, but I doubt many would agree. But mainly, if I understood you right, you didn't have a solution yet. I told you that you could turn coins over- just that you couldn't mark them.

Secondly- I told you that your explanation was so hard to follow that it could have been right, but you didn't submit it as such, so I didn't hurt my brain proof-reading it for flaws as a solution.

Finally, You were not following the same solution as I posted. I also posted that that was only ONE solution out of many, so you are free to pursue the path you were on with your new understanding of the rules. Besides- what about 5 on a side?

 

[itsid]

BTW- Sid,

A couple of things : I never said you couldn't describe the coins as A or B, just that I was getting confused and I thought you could describe the solution so it could be better understood by describing their locations and movements rather than labeling. I reposted your original solution in that manner as an example. You thought it was easier to understand your way, but I doubt many would agree. But mainly, if I understood you right, you didn't have a solution yet. I told you that you could turn coins over- just that you couldn't mark them.

This is a rather technical process, basically interesecting (if/then/else) statements I could faster write the process as code than describing it with words
I think with labeling weighings with roman numerals (bold) and outcomes with a and b to track the individual step would help to understand.
I can't describe it any better than I did, I'm sorry...

But let me say: it's hard for me to follow your description too
keeping track of now heavier side once lighter side and such is harder for my brain than to simply say B-coin heavy side, knowing the B was the lighter side in the last weighing.

I know you were okay with labelling my groups to track them in the description though
And that was easier for me to describe a process like this.
And descriptions are always a pain to read.
Try to describe how to bind laces using nothing but words...
that is a pain to read aswell

Secondly- I told you that your explanation was so hard to follow that it could have been right, but you didn't submit it as such, so I didn't hurt my brain proof-reading it for flaws as a solution.

I don't think it's that hard to follow
with the labelling (roman numerals, a or b outcome) and moving along.
But I could be wrong; again I'm sorry I can't do any better.
I assure you, there is no flaw in my process, other than the marking of lighter coin on heavier side (exactly as you did just with fewer coins)

Finally, You were not following the same solution as I posted. I also posted that that was only ONE solution out of many, so you are free to pursue the path you were on with your new understanding of the rules. Besides- what about 5 on a side?

I did not, I used fewer coins for the second step,
six instead of eight on the scale, two instead of three in front of the scale.
other than that it's basically the exact same idea..
(well as far as I can tell.. I still am unable to follow your description yet.)
and the third step is accordingly much easier to follow (for me ) since I only have either one or two coins;
if one (I know it's fake but not if heavier or lighter)->check against valid coin
if two (I know it's heavier but not which one)->compare against each other

'sid

 

[Poboy kartman]

Sid- I think we have a misunderstanding due to an error in translation or else you just didn't understand me. MARKING and TRACKING are two different things. Again- the rules are simple- they haven't changed nor did I ever say you broke them or "cheated". I did say the internet solution was out of bounds because IIRC- it started out with " mark the coins....." you cannot mark them if all you have is a balance scale.

LABELING has a dual meaning in English: you can "label" a person who drinks too much a drunk. (In other words you can "name" someone or something in a particular way). LABELING can also mean attaching a printed label or just writing a designation on something. One.is physical, the other verbal.

The internet solution didn't violate the rules per se, if it was phrased as "to describe the position of this coin, we'll call it A." Even so when you are supposed to mentally label 12 coins and track their individual movements with as many moves as they took, I think that is a solution that only works for a small percentage of the population. To put it another way- if the puzzle is how do you know what is going to happen and the answer is you just know- and the question and answer are both supplied by a clairvoyant- snot really a puzzle!

ANYWAY- This is the big question Sid, do you think you posted a viable solution. If so- I will I will check it and if I don't find any flaws (where it's possible that the counterfeit coin could be undetected)- I will declare it a solution, because as I never said it violated the rules- it was just harder to understand than I thought it needed to be.

 

[itsid]

Sid- I think we have a misunderstanding due to an error in translation or else you just didn't understand me. MARKING and TRACKING are two different things. Again- the rules are simple- they haven't changed nor did I ever say you broke them or "cheated". I did say the internet solution was out of bounds because IIRC- it started out with " mark the coins....." you cannot mark them if all you have is a balance scale.

LABELING has a dual meaning in English: you can "label" a person who drinks too much a drunk. (In other words you can "name" someone or something in a particular way). LABELING can also mean attaching a printed label or just writing a designation on something. One.is physical, the other verbal.

The internet solution didn't violate the rules per se, if it was phrased as "to describe the position of this coin, we'll call it A." Even so when you are supposed to mentally label 12 coins and track their individual movements with as many moves as they took, I think that is a solution that only works for a small percentage of the population. To put it another way- if the puzzle is how do you know what is going to happen and the answer is you just know- and the question and answer are both supplied by a clairvoyant- snot really a puzzle!

ANYWAY- This is the big question Sid, do you think you posted a viable solution. If so- I will I will check it and if I don't find any flaws (where it's possible that the counterfeit coin could be undetected)- I will declare it a solution, because as I never said it violated the rules- it was just harder to understand than I thought it needed to be.

I know that marking and tracking are two different things.
But in a description in order to fullfill the given task,
it's the same thing.
since it doesn't matter if I colour it differently, or just remember that it had a dent on it's edge.
Not a single one of this coins is a real thing, so I cannot label them, mark them or track them other than "in my mind" virtually.
The virtual marking has no effect other than keeping up with the description someone else wrote down,
or in this case.. to help others following the description when reading my (or your) description
A virtual marking is the same as a virtual tracking.
different terms for different actions in real world, for a mind puzzle without real objects: same thing.

And that's why I thought: "Without knowing what coin it was that was on the lighter side previously"

And, again, my solution is correct (just as yours) I just use fewer coins.
You'll not find a flaw.
Just keep in mind at one point i say let's assume I do know by laying all A coins face up and all B coins face down...
That applies to the SECOND weighing, not the third.
But it's only important for this worst case scenario (the scale is NOT balanced in the second go, that's why I mentioned it late. under II.b)

To keep track again:

I
roman numeral followed by bold text is a weighing proces
I.a.
is the outcome (balanced)
followed by roman II for this case then roman III

I.b.
is the outcome (unbalanced)
followed by roman II for this case and so on

'sid

 

[Poboy kartman]

OK- Sid

I'll try one more time to explain this. You still have a different interpretation of what I mean by marking the coins. Of course the coins and scale don't exsist,but what I meant was you could not alter the physical appearance of the coins. Technically, you could take the tray off the scale and scratch the coins- but technically I solved your puzzle twice following the rules. But realistically when someone says marking, it involves a pen which is outside of the rules.

Keep in mind, if you'll go back, you'll see I never said you didn't solve. I told you turning over coins was perfectly acceptable. I misinterpreted the last part of your post as I thought you needed to think more because you couldn't solve without physically marking the coins.

I have gone back and studied your solution and I find no flaws in the solution or the methods used to achieve said results. I think tomorrow I will re-post your solution in different words like I did your balanced solution, because via PMs I have found I was not alone in having difficulty following your explanation.

So now that's 2-( 3 if you want to count the internet solution)........

It's been so long that I can't remember how many I came up with, but it was quite a few. And the different solutions come back sooner or later to help solve when you don't start 4 and 4. I said I didn't know if I turned coins over or not- I know I did, just don't remember when. I'm thinking it was when you start 6 on a side- ( I think I solved it that way- but maybe I didn't solve 6).

Anyway, I'm pretty sure that I solved it starting with something other than 4 or 5.

 

[itsid]

OK- Sid

I'll try one more time to explain this. You still have a different interpretation of what I mean by marking the coins. Of course the coins and scale don't exsist,but what I meant was you could not alter the physical appearance of the coins. Technically, .... it involves a pen which is outside of the rules.
...

We have different interpretations of mind-puzzles, yes.
when someone says, mark a non existing coin,
I understand (remember closely said coin)
and that is exactly the same as "keep close track of this very coin"

and as you said "you mustn't mark"
I understood:
"you cannot tell any coin from any other as soon as it is in a specific group"
so all the coins on the table are indifferent,
all the coins on the left of the scale are indifferent,
all the coins on the right...
and all in "my box" of valid coins.

we both cannot fullfill that task (it's undoable!!!)
So yeah, we both cheated regarding your "no marking" rule.
since we didn't say "use a pen" but we said "keep track of this and that"
and for a mind puzzle it's the same thing
Both sentences are practically the same thing.
"you have two blue and one red ball, find the red one"
"you have three blue balls, find the one in the middle"
both require a different visualisation, but both times you'll find the correct ball in no time.

what I meant was you could not alter the physical appearance of the coins.

There is no physical appearance one could alter.
a virtual alteration only serves the purpose of tracking the item under a certain circumstance.
Or in our case, to try to make it easier for others to follow using a description.

Anyways... if you want to disagree let me know,
we then start this conversation in german ...
mir fällt es nämlich deutlich leichter Dir die Vorgehensweise in meiner Muttersprache zu erklären
*gg*

Oh, I never said you dismissed my solution,
but it's violating your previous rule (as much as yours),

Now.. let's just stop this BS..

solve my coin puzzle.

you get blindfolded and in front of you, there are twelve coins, six facing up, six down.
you cannot tell by feeling them which way is which...
you're given the task to divide the unsorted coins into two groups, each of them has to have the same amount of coins facing up...
what do you do?

no backdoors!
"blindfolded" means you are, not "remove blindfold at wish"
"same amount of coins facing up" means "there are coins facing up or down" in the end.

just add "you are only allowed to touch eight coins nothing else"
as a rule (still solvable)

'sid

 

[Poboy kartman]

I cannot mark, but I can seperate them, right? I need nothing but a box to put original coins in
(together with the table for possible fake coins and scale for.. well scaling )

Well I'll try.

I make three groups A, B and C with four coins each

Best Case scenario
I.a.
balancing A against B is levelled
All coins on the scale go into my box of original coins.
The coin is in the remaining group of four.

II.
balancing three coins of the last group against three coins known to be valid
leave one coin on the table
II.a.
BALANCED scale:
the last coin not in the box, nor on the scale is the fake coin.
III.
balance fake coin against real coin to know if it's lighter or heavier

II.b.
UNBALANCED scale:
I now know if the coin is lighter or heavier. (just say heavier here)
III.
weigh two of the three possible fake coins against each other
the other on the table (rest into the box)
III.a.
BALANCED scale:
the last coin is the fake coin (and I know it's the heavier one)
III.b.
UNBALANCED scale:
the last coin is the heavier one on the scale.

second scenario:
I.b.
balancing A against B is NOT levelled (let's just say A is heavier; if not I change the names A->B & B<-A )
the remaining coins on the table go into my box of original coins.

II.
three coins on both sides of the scale two from group A and one of group B each.
the other two (B-) coins stay on the table.

II.a.
BALANCED scale:
I now know that the fake coin is lighter (since it was a B-coin previously)
and that it is still on the table
III
weigh the coins on the table against each other.. the lighter is fake

II.b.
UNBALANCED scale:
Now it's getting messy.. since I think I need to know if the coins are from the A or the B group originally,
but without a marking that seems rather impossible.

let's assume I do know by laying all A coins face up and all B coins face down...
III.
measure the two formerly A-group coins of the HEAVIER side
lay the B-coin of the other group on the table (rest into the box)
III.a.
BALANCED scale:
the fake coin is the one 'lighter' coin of the formerly B group from the second go.
III.b.
UNBALANCED scale:
the fake coin is the heavier coin on the scale.

If I do not mark the coins in the second process I don't know, I need to think of it some more

'sid

Sid- I've still thought about the blindfold puzzle but I've given up on it.

OK- Sid's solution in other words: I won't bother with the balanced scale because it's already been described 2 ways.

So I'm just going to deal with the unbalanced scale. To simplify (imho) - let's say from the start that there is a heavy side of the scale and a light one and turn all the coins on the light side heads up and the heavy heads down.

So: Take two of the heads up coins off the light side of the scale and put them in front of that side of the scale. Take one of the remaining heads up coins and put it in front of the heavy side of the scale. Take two of the heads down coins and put them on top of the heads up coin on the light side. Put the heads up coin in front of the heavy side of the scale on top of the two remaining heads down coins on the heavy side. So you now have 1 heads up and 2 heads down on each side of the scale and two heads up coins in front of the light side of the scale. You also have a stack of 4 coins off to the side that were never weighed and are genuine.

So: If the scale is now balanced, everything on it is genuine. Take off everything but one coin.Take one of the 2 coins from in front of the scale and weigh it against the genuine one you left on the scale. If the scale balances then the fake is on the table and it's light . If it doesn't balance the fake is on the light side of the scale.

Back to 3 on a side- The scale remains unchanged: everything has been eliminated except the one heads up coin on the light side and the two heads down on the heavy side. Put everything else aside.Put the heads up coin in front of the scale and weigh the two heads down against each other. If they balance the fake coin is on the table and it's light (heads up. ) If the scale doesn't balance, the fake is the heavier of the 2.

Final scenario: The light side of the scale now goes down. You have eliminated everything except the one heads up coin on the side that used to be heavy and the two heads down on the side that used to be light and is now down. The solution is the same as described above.

While Sid's explanation was correct- it really wasn't too clear to me on the last step.

Anyway- now you have 2 explanations for the same solution- hopefully one or the other will be easy to understand for you.

Now about that 5 on each side or another solution for 4 on each side or.........

 

[itsid]

Okay, "my" coin question.
again it's a really easy solution, two sentences basically
And if you actually try it with 12 coins at home without a blindfold (to see what happens)
and look at your coins at home, you'll notice something.
If 20h from now nobody posts his answer, I'll post the solution.

'sid