# A well balanced puzzle: Logic puzzle(s) in visual disguise

This is a rather involved puzzle and might require a bit of stamina. All of the puzzle is in image form. The introduction text is not needed for the puzzle. At the end of the puzzle you'll get a short English sentence. The puzzle consists of several sub-puzzles and you're encouraged to post solutions to the individual steps - I will comment on them.

The puzzles has now been fully solved, and the complete solution is summarized in the accepted answer.

# Introduction

You're in a circular room with a dome-like ceiling. All walls and the floor are bright white. There is only a single, metal door, which has a small, circular whole in eye height. You don't have any recollection how you came here, but at the moment, you're really only interested in getting out. The door, is looked. You knock, and there is some movement behind the hole. Somebody comes to the door and talks through the hole. The voice, however, sound foreign and not very human: "You awake? You out? You say passphrase!"
You are about to ask something, when suddenly the walls behind you begin to shimmer and form a series of images, and the voice through the door adds: "You clever? You find passphrase."
Whatever else you say to your capturer, the only answer you get is: "No, not passphrase."
It seems you really have to find the passphrase. You just hope you can, before you die of hunger and thirst.

On the wall around you, the following images can be found (The appear clockwise around the room starting with the door and ending with the door.)

# The puzzle

(Instruction 1)

(Instruction 2)

(Instruction 3)

(The bottles)

(The scale)

(The code)

(The keys)

The following image is auxiliary for convenience sake. It is a close-up of the bottle labels of the 2nd image above.

(Bottle Label close-up)

As always, I'm interested in your ideas and feedback. In particular, I hope the puzzle is fun. If it isn't, let me know why. If it turns out that the puzzles needs amendments or changes to become better, I'll edit them.

# Notes:

The red ABCDEF/1234 labels are not required for the puzzle. They have only been added to make it easier to discuss/describe solutions.

The 6 'rod-shaped' objects in the last image fit in size into the 'slot' of the image with the letters above it. (As shown in the smaller black & white image.)

You may use any tool etc. to solve this puzzle, but it should be perfectly possible to do this with pen & paper alone.

## HINTS

If you are really stuck with this puzzle and are wondering along the lines of "What the @£! am I supposed to solve here??" you may look at the following hints. But they will spoil a bit of your fun (as all hints do.) I try to make successive hints revealing more and more, so just try one at the time...

Where am I even supposed to start this??

The first images until the first horizontal line are called instructions for a reason. Try interpreting them in terms of what is this puzzle about? and what am I to do?

I still don't get it at all...

Remember: At the very end of the puzzle is a pass-phrase. The only image with letters is obviously important, but how could one encode with it - using the previous images? It surely can't be done with one image alone...

But... There are endless possibilities! I could read anything out of this...

Really? Is there no clue about the length of the pass-phrase? Does this length match anything... ?

Okay, okay, so what do I have to solve first ?

The puzzle has 3 main-sub puzzles. Guess what, they are sorted that way. Let's call them the bottles, the scale and the code puzzle. The scale is (literally!) the central puzzle here. It provides the information needed to solve the code. But in order to attempt the scale you need information provided in the bottles. What could that be? Have another look at the instructions! What do the yellow squares symbolize? What does the blue-to-grey shading symbolize? So what could the labels then be for?

All nice and well, but can you give me another hint?

NO. If you are still stuck and don't want to spent more time on thinking, you might as well read the accepted solution below!

• Wow, I have no idea of the answer yet, but top marks for effort! – A E Dec 27 '14 at 18:27
• @AE Thanks. Yes, it took me the last 3 weeks (on & off) to build this. It might be faster to solve than to build ;c) – BmyGuest Dec 27 '14 at 18:35
• I haven't even started to think what the pictures mean, but I'm intrigued already. They are a pleasure to behold even at a first glance. Your puzzles are a visual language in themselves! – xnor Dec 28 '14 at 19:09
• This really is the most weird and wacky puzzle I've ever seen. I've no idea how to proceed with it, but will be very interested to see the solution! – Rand al'Thor Dec 30 '14 at 15:55
• I really wish this amazing puzzle would receive more attention. Really well thought out. Thank you for your time. – user1853181 Jan 18 '15 at 1:10

This is a community-wiki answer compiling the final solution of the puzzle.
It also presents the solution as intended.
The solutions were found by individual answer posters.

For the impatient, the final answer is:

"Balance is the rectifier"

Individual contributions were:

Gary Ye:
- First discovery of mechanism of part 1 (The Bottles)

i_turo:
- The full solution to part 1 (The Bottles)

EFrog:
- Final sorting detail of part 1 (The Bottles)
- Valuable ideas on how part 1 and part 2 are related.

Bulldogg6404:
- The mechanism of part 2 (The Scales)

Nephtyz:
- The first solution to part 2 (The Scales)

Bulldogg6404:
- Missing colours on the scales. (The Code)
- The mechanism and solution of part 3 (The Code)

# Detailed Solution

## Instructions

• All images: The blue-to-grey gradient everywhere represents:

order. Otherwise identical bottles (they are all blue) have to be sorted in some way and then be used in this order.
Also: The final pass-phrase is gotten letter by letter in correct order.

• Instruction 1 (left part)

The original grid of bottles is not in order. The labels and the yellow code-grid-table need to be used to achieve sorting. For the meaning of the code-grid-table see 'The Bottles'.

• Instruction 1 (right part)

Bottles are labelled by dots, indicating the amount of liquid they contain. Filling a bottle into a tube will fill the equal amount of square grids, starting from the further most grid. Other details to be seen: The liquid does not level out across neighbouring squares. The spacing or alignment of 'dots' on the labels is of no consequence. (The shown bottle has 5 dots in an arrangement none of the bottle labels has.)

• Instruction 2

The 24 bottles are needed in 'The scales'. They are used in the order determined by 'The Bottles'. They need to be filled into a single tube one after the other, while the hanging weight is moved at each step to keep the scales in balance.

• Instruction 3

One key is the final puzzle piece. It is needed to complete the second part (The Scales). This single key needs to be inserted into the code-table. The pass-phrase is found letter-by-letter from the grid. There are as many letters as there are bottles (24), and their order is the same as determined by the first part (The Bottles).

## The Bottles (solved)

The aim of the bottle puzzle is to bring the 24 labelled bottles into correct order.
The brown bottle labels are a transparent grid. If all are overlaid, only a single square remains fully transparent.
It is only possible to remove a specific label from the stack in order to get a second transparent square. (Removing any other label doesn't change the situation.)
Once that label is removed, there is only a single specific label which can be removed in order to get a third transparent square. etc. etc.
This gives an order of labels. However, it is ambiguous as it is not clear if the order is first-to-last, or last-to-first.
Checking the position of the "first" and the "last" transparent grid-square on the yellow code-table of hint reveals: Alpha and Omega.
Alpha and Omega are the first and last characters of the ancient Greek alphabet. They are often used (f.e. in religion) to indicate Beginning and End.
Therefore the correct order of bottles is with the first label removed showing 2 fields and the next showing 3 fields etc. As all bottles are equal except the grid and dot labels, and the grid has been 'used up' by the puzzle now. The 'dots' are all that remain. 'Dot-labels' sorted by the order determined above are:

Spaces in the dot-labels are decoys and can be ignored.
The number of dots in sequence (ignoring any spaces) are:
5; 3; 7; 2; 4; 3; 4; 4; 5; 2; 3; 1; 6; 2; 3; 4; 6; 5; 6; 2; 1; 4; 4; 7

## The Scales (solved)

The balance of the scale is determined by

the total weight of filled pipes and the hanging weights.
Each 'filled square' counts for the same weight, and the tipping moment is determined by the (horizontal) distance from the centre point multiplied by the (summed) weight at this distance.
An example (tipping to the right by "+2"):

Following Instructions 1, it is the aim of the puzzle to ...

...fill in the bottles one after the other into either of the 6 tubes, while keeping the system in balance with the hanging weight. The exact sequence has to be found by the puzzle! However, the order of the bottles is given (by the The Bottles puzzle) and there is only a very limited number of possibilities which can keep the system in balance at each step.

Following all of the above, the puzzle solves into the following sequence:

Read the image left to right and top to bottom for the sequence of 24 bottles subsequently filling the pipes:

A second solution is possible, which has bottles 11 and 15 swapped. However, only one of the two solutions (the one above) will produced an English pass-phrase in the third part of the puzzle (The Code).

## The Code (solved)

The solution of part 1 and part 2 of the puzzle give one

24 ordered actions of pouring bottles into the grid. Each pouring-actions is defined by 2 things: A tube colour into which the liquid is filled and a hanging position for the balancing weight. This position is associated with a colour, but some positions are missing.

The missing (b&w checkboard pattern) fields on the scale can be found by

looking at colours of all keys. All 6 keys show the same colour 'pairs' albeit in different vertical ordering. The according colour pairs appear in symmetric position on the scale as well, allowing to fill in the spots as with the following image:

Also: Colour-pairs (if watches as RGB hex-codes) add up to FFFFFF, i.e. are complementary.

Labelling the 26 weight-hanging positions from the left to the right, one gets the solution as a table:

To find the appropriate key for The Code one has to...

...realized that the final situation after pouring all bottles left exactly two red squares empty. On the bottle, the squares are represented by yellow diamonds. The same dots appear on the keys, so the two yellow diamonds on the red key will 'complete' the puzzle as hinted at by 'Instruction 3'.

With this key inserted into the code-table...

...one can now translate the 24 pairs of 'pipe colour' and 'weight position' into letters by looking them up in the grid:

This eventually leads to the 24-characters of the pass-phrase:

BALANCE/IS/THE/RECTIFIER

# 1. General

## 1.1. Instruction 1

What to do with INSTRUCTION 1 has already been discussed by "rand al'thor" and "Tryth" in general. Just for clarity, here again the basic idea with the terms I'll use in my answer:

• blue shading: the blue shading of the bottles (and also the code in INSTRUCTION 3)
• labels: the 8x8 grids with holes on every bottle
• yellow dots: the yellow dots on every bottle
• code-grid: the 8x8 grid with the odd symbols

Summarized I think the image tells us to empty the bottles in the right order through the right tube/color into the scale filling a certain amount of squares.

# 2. Proposed Solutions (partial)

### 2.1. Order of Bottles (verified)

This solution was figured out with the help of "Gary Ye's" essential observation!

The first question to ask is whether the order of the bottles is actually important. The answer is YES.

The blue shading of the bottles in INSTRUCTION 1 and the same shading of the letters in INSTRUCTION 3 clearly indicate a connection between a bottle and a letter of the password, i.e. every bottle corresponds to exactly one letter of the solution. And since the letter order in the solution is obviously essential, so is the order of the bottles.

Although the blue shading indicates that the order is important it does NOT indicate that the darkest blue bottle is indeed the first one! So the order must be hidden in some other attributes of the bottles. Considering that the order must be unique and non ambiguous, the yellow dots can be ruled out and therefore only the labels remain.

The important thing to observe here is that some pieces in the 8x8 label-grid are missing (i.e. not white or any other color, but missing). This means if we put them over the 8x8 code-grid some symbols will shine through. Even more important, if we put two or more labels on top of each other some symbols will still shine through. And this is exactly how the order is defined.

For reconstructing the order of the bottles the symbols in the grid don't matter all that much. The procedure looks the following:

1. Choose a label that has exactly 24 (the number of bottles and the number in the order) empty squares and put it on the grid, E4. There are now exactly 24 symbols visible. (There are multiple options for the first step, but only one allows successful continuation.)
2. Choose the next label so that when it is put over the first one there are still exactly 23 symbols visible, A2.
3. Repeat the same process for the remaining labels so that 22, 21, 20, 19, ..., 1 symbols are visible.
4. This is the order of the bottles with the top one being the first. Note that the last visible symbol is A (or Alpha) whereas the 24th symbol is Omega. That might be an indication of the otherwise arbitrary seeming choice in step 1.

eventually resulting in:

 8 7  21 10  3  6
2 13 17 22 20 11
4 14  9 16  5 18
23 15 19 12  1 24


This completes the code-square and the labels (and probably also the blue shading).

# 3. Further Ideas

### 3.1 Tubes

Now that we know the order in which the bottles have to be emptied, the next thing we have to figure out, is through which tubes to empty the bottles.

Assuming that the labels, the shading and the code-grid are already completed, likely the yellow dots contain this information. Especially considering that the first bottle has exactly 5 yellow squares and INSTRUCTION 2 shows that the first bottle must be emptied through the 5th tube.

Considering that figuring out the order was rather tricky, this might be a little bit to o simple though ... I would guess that the spaces between those dots are also really significant (as they were in the labels), but I don't have any concrete ideas about that at the moment.

### 3.2 Amount of Squares

Considering that there are almost no instructions left for the bottles, the amount of squares to fill by every bottle might even be constant, or actually maybe 1.

The only real other possibility I can see is that the yellow dots could indeed describe both the tube and the amount of squares.

• You've excellently cracked 99.9% of the bottle puzzle. (Please use spoilers for the essential points). However: The yellow grid is not completely useless. There is one more ambiguity in the order which isn't covered by your reasoning. Or rather: you've made choice there which was arbitrary... As for the scale puzzle, I'll let you (and others) ponder it for a while and don't comment on your suggestions yet. – BmyGuest Jan 12 '15 at 22:08

GENERAL DISCUSSION

Following Tryth's terminology, let's name the images as follows:

• INSTRUCTION1
• INSTRUCTION2
• INSTRUCTION3
• BOTTLES
• SCALES
• CODE TABLE
• KEYS
• LABELS

LABELS isn't really important, just there to help us with BOTTLES. The OP has intimated that SCALE is the key to the whole thing, so let's take a careful look at SCALES. We have six tubes, labelled by different colours, from which liquid drips down into six pipes, which lead to different points a balancing scales with two small grey weights on each end and more odd colours.

Look at INSTRUCTION1. The left half is still a mystery to me, but the right half shows bottles being emptied into a tube of the same type as those on the scales. There are 5 bottles full of greyish-blue stuff, and 5 squares coloured greyish-blue, so I suspect each bottle in BOTTLES is going to fill up one of the small squares in SCALES after being poured through one of the tubes at the top.

Now INSTRUCTION2. We have a sequence of 24 bottles (the same number as in BOTTLES), and two more of those small grey weights. The first bottle at least gets poured into the 5th of the 6 tubes. The scales end up tipping one way or the other.

What about INSTRUCTION3? We have a miniature version of SCALES printed on a big square, from which one corner in the shape of a jigsaw puzzle piece has been removed. This piece has a key on it, in the shape of one of those in KEYS. The piece is placed in a circle of 6 keys, one of which is chosen and inserted into what looks like CODE TABLE. Five cells in this table then have colours like those of the five outstanding bottles in INSTRUCTION1.

So here's what I think we need to do:

• decipher the squares and yellow dots in BOTTLES (reproduced in LABELS) into colours (a hunch)
• empty all 24 bottles into the tubes in SCALES, using the colours we've found to determine which tube each one gets poured through
• notice which way the scale tips, and use this somehow to deduce which of the KEYS to choose
• insert the chosen key into the CODE TABLE, and pick out a few cells somehow whose letters reorganise to give the passphrase

SOME SPECIFICS (PROBABLY WRONG)

In the second image, the yellow dots under the bottles translate to:

1011010 1011010 0001000 0001100 1111111 1101000
1110000 0011111 1110111 0001111 1000100 0011100
1100000 1010000 1101011 1101100 1111000 1101101
1110100 1001001 1110111 1000000 1011110 1111011

I now suspect the squares on the bottles are something to do with colour codes (for which there are several different conventions).

• That's binary, not base64. Decimal equivalent is 90 90 8 12 127 104 112 31 119 15 68 28 96 80 107 108 120 109 116 73 119 64 94 123. – A E Dec 27 '14 at 19:05
• I'm somewhat skeptical about your second hypothesis. Do an image search for instances of the entity you mentioned, and note that they all have a specific signature in the corner(s). This is necessary to uniquely identify the entities (it establishes a reference point for scale). – wchargin Dec 27 '14 at 23:44
• I don't understand why the first picture means the binary numbers you found. Can you please explain your thinking for that step? – Kevin Dec 29 '14 at 9:35
• @Kevin - It's now no longer the first image, but the yellow dots under the bottles in the second image. The OP was edited! – Rand al'Thor Dec 29 '14 at 11:28
• After you have emptied a bottle, and it's contents have been separated adding weight to the scale, you have to move the grey weights to the appropriate positions to get the scale to balance again? Once the scale is balanced you should be able to read the passcode based on the colors provided? – YoungJohn Jan 9 '15 at 17:24

I spotted that many of the 8x8 grids contained in the bottles have very similar patterns.

I have summed up the grids, by saying white = 1 and black = 0, and I received the following interesting but definitely not random pattern in which the numbers 0 to 24 all occur once (except for 1 and 2; 2 occurs twice).

This gives:

21  1  1  1  1  1 19  2
1  1  1  1 10  1  1 12
1  1  1 14 15  1  2  1
1 17  1  7  1 11 23  1
5 13 20 24  1 22  4  1
1  1  1  9  1  1  1  6
1  8  1 16  1  1  1  1
1  0  1  1 18  3  1  1

• Very important observation. Well done. Maybe put the info into a spoiler tag, though. – BmyGuest Jan 9 '15 at 15:51
• Other question: Do you have a suspicion what the bottle-puzzle is all about? i.e. what is it, you want to find out by the labels? This would be an important first/next step. And is there any connection to the instructions image? – BmyGuest Jan 10 '15 at 21:01

I'm thinking that the symbols 8x8 grid is a big clue, I'm not 100% sure, but I think, that every symbol stands for a character, I didn't get very far till now, but I got a few symbols substituted by what I think the meaning of them are. I also think, that if you have all, you can overlay the bottles 8x8 grids over it and get hints for INSTRUCTION 1.

For now i have these substitutions:

         t |   |   | V |   |   |   | F |
g |   | y |   | pi| q |   |   |
P |   | zu| D | j | S |   | d |
| E |   | S | H |   | J |   |
s |   |   | A |   | r |   |   |
| Q | H |   | h |   | X | c |
|   |   | z |   | p |   |   |
| d |   |   | n |   | W |   |


Most of the substitutions I found in the font called Symbols in Microsoft Word. Some of the Japanese characters I knew myself.

• Indeed a very interesting out of the box approach. – Gary Ye Jan 10 '15 at 22:51

This is more of a brain dump at the moment, but hopefully it can help someone.

The images are 'named' (as in the alt text) as follows (in order):

• INSTRUCTION1
• INSTRUCTION2
• INSTRUCTION3
• BOTTLES
• SCALE
• CODE TABLE
• KEYS
• ( LABELS )

This, if not anything else, might indicate that

The last image is a key for the second last - the color at the top indicates for which columns the colors are a key, and the left column of colors is a key for the left column of the code, and ditto for the right.

The BOTTLES ( LABELS ) image has a series of 8x8 grids with holes in - this most likely corresponds to the 8x8 grid of symbols in the INSTRUCTION1 image. How, I don't know.

Note in the INSTRUCTION1 image,

at the top left there are 6 bottles not colored the same. I have labelled them starting from the most blue.

These correspond to the grid coordinates C2, E4, A1, B4, F1 and A3 respectively. These also might correspond to the six colors in the code in the SACLE image.
I did not get anything useful by overlaying the holed grids that correspond to those coordinates onto the symbol grid. But maybe I just didn't notice a pattern.

Here's a transcription of the CODE TABLE image:

WHOGTX FVTOJ/
ROSSIU ZTHXIC
/PYNNW ETUG//
DENFIZ TTOEMW
AVBAEJ UZRZFI
WVTGYE ZHKXPR
MI/HJZ RWULBL
EFDTS/ Z/OGZE
FSSUFY WLEYAZ
IUXKXT VTPLED
TKVATE A/OYYU
FOHI/B SGH/RZ


Here's a frequency analysis. Odd how there are so many Zs.

 E  T  Z  F  I  O  U  A  G  H  S  W  Y  L  M  P  R  V  X  D  K  B  J  N  C  Q
12 12 10  7  7  7  7  6  6  6  6  6  6  5  5  5  5  5  5  4  4  3  3  3  1  0


The puzzle might even be able to be broken with cryptanalysis of the code.

In the KEYS image:

The colors in the left and right columns are always the same, just in a different order. This would lead me to conjecture that one must use this color key to reorder the corresponding column in the CODE TABLE image, after which something will be spelled out. These colors also correspond to the ones on the scale in the SCALE image.

This is all I've got for now.

• @BmyGuest Do you mean the new fifth image (diamonds at the top, lots of coloured rectangles) or the old fifth image (the one with lots of letters)? – Rand al'Thor Dec 29 '14 at 13:18
• I've edited the post to have the new image order properly represented in this 'answer'. This also changes my original comment to "Nice ideas. I haven't seen any ideas about the SCALE image yet, though. This is rather the 'central' part of the puzzle." – BmyGuest Dec 30 '14 at 15:49

Ok. I've mostly been following this thread from my phone while I'm at work, so I haven't managed to read most of the work already done.

A few details I haven't seen mentioned (though I could have overlooked them):

The hanging weight on the scale seems to be movable. And I'm guessing that given that the weights are divided in two segments, these weights probably equal the weight of two square-units-worth of liquid. Unfortunately, I don't know how weights and scales work in regard to distance from the center.

Also:

The diamonds on the top of the key are the same as the diamonds on the labels on the bottle. This probably indicates which tube the bottle is meant to be poured into.

My guess regarding the shading of the bottles:

The right-hand side of "Instruction 1" seems to indicate that the first (darkest) bottle will fill up five square-units. Using this information, it's not unreasonable to suspect that the next-lightest bottle will fill up four SU, then three, down to one SU for all of the grey bottles.

So. Given that information, this is my hypothesis regarding actually solving the passphrase:

First:

Using the labels, we can determine (as @i_turo has shown) the order in which the bottles should be used. By overlaying the labels onto the 8x8 grid in "Instruction 1", we see that it slowly covers up (what I'm assuming is the entire Greek alphabet, as most of the characters I know are in the grid, and the Greek alphabet contains 24 letters) the symbols in reverse from Omega to Alpha. The opposite order (A > Z) should probably be used to pour the bottles.

Second:

2.) Now that we know what order to put the bottles in, we have to determine which tube we pour them down. This is most likely determined by the yellow diamonds on the labels, as they correspond with the colors on the keys. Unfortunately, I'm not good with codes like this so I'm not sure what to do. But we need to find a way to translate the label-diamonds into colors somehow. We do know, however, that there are only six color-tubes while there are 24 different layouts of diamonds. So either the colors can be represented multiple ways using this code, or the code changes each time we remove a key and replace it.

My hypothesis regarding this...

...is that the six keys begin in a line (Red, Yellow, Green, Cyan, Blue, Purple). If you line up all of the keys and allow each 2nd-diamond to correspond with the 1st-diamond on the next key, you have a pattern of AB BC CD DE EF FG. This gives you 7 diamonds overall (the number that appears in the labels), ABCDEFG. Once we remove the blue key (now EF) to use it in a moment, we slide the keys over, then replace the blue key at the END of the line (making it now FG and purple becomes EF). Then we use that arrangement to determine the color for the next bottle.

Third:

When we pour the bottle into the tube, it will fill up the squares in the row corresponding to the tube color, as shown in "The Scale". We can determine how many squares will be filled up by using the blue shading, as earlier discussed. Since bottle E4 is first, and it appears to have a color matching that of the first bottle in "Instruction 1", we can assume it contains 5 SU of water. So when we pour E4 into the blue tube, the scale will tip to the right.

Fourth:

When the scale tips, we have to move the hanging weight to make it balance again. The free-standing weight is clearly fixed in place. So we have to play with the hanging weights until the scale becomes balanced, then look at which section of the scale the hanging weight is occupying.

Fifth:

We insert the key whose color corresponds with the tube through which we poured the water into "The Code". Then we find the letter at the cross-section between the color of the space the hanging weight is occupying (indicated on the key itself) and the color of the key/tube that we used (indicated by the columns in "The Code"). That gives us our first letter. We repeat this process until we're done. The final result may still be in some kind of code, though that doesn't seem to be indicated anywhere in the pictures.

A concern/question for @Bmyguest:

The picture that @Tryth shows indicates that there are six differently-colored bottles of liquid instead of five, as all of the other pictures with shading show. This would imply that the C2 bottle contains 6 SU of water (or that 2 of the bottles have matching colors). If that's the case, then why is that sixth colored bottle not shown in the other pictures, specifically the ! speech-cloud in "Instruction 3"?

• Thanks for your input EFrog. Reading through it, there are some gems but also some complete fails. I'm not telling which is which though. (But some points are very valid.) Most notably (and thank you for that) I've again realized that one image isn't 100% clear enough to prevent misinterpretation. I will modify and edit accordingly soon. – BmyGuest Jan 13 '15 at 13:59
• @BmyGuest Ok, fixed I think. Lol – EFrog Jan 13 '15 at 14:37
• @BmyGuest I'm afraid not. If I had the physical pieces to the puzzle I might be able to get somewhere. My primary hang-up is the weights. Idk how to determine how far each side will tilt when I move the hanging weight. – EFrog Jan 21 '15 at 9:47
• Simple physics of rotational moment: Force = weight * distance from rotational centre. Or look up lever(en.wikipedia.org/wiki/Lever) – BmyGuest Jan 21 '15 at 10:14

Feb 8th edit:

Some more progress has been made since I posted this answer, now I'm choosing to edit it to reflect what we know. I used the keys to finish the scale's color spectrum base; the edited scale has been added by Bmy to the wiki answer with an explanation of the logic involved.

The issue we are facing now is deciding which tubes the bottle contents need to go into. We have supposedly used up the meaning of the 8x8 grid, where it was relevant to determining order. The yellow diamonds are the only label we have not fully understood from the first instruction, and it is believed that this is where we will determine the placement of the contents.

My current line of thinking holds that the yellow diamonds tell us the amount that the respective bottles will put into the tubes. This is supported both by my counting (95 empty tube spaces, 93 diamonds) and by Bmy's upvote. However, if this were all that the diamonds tell us, then we would still have no information on which tubes to fill. The only piece I can imagine being useful is the spacing between the diamonds. It has been made clear that the labels are supposed to be center-aligned, and thus the left/right sides of the diamonds don't mean anything. Only the spacing /between/ them seems to matter here, though it could still be that it has no meaning at all. In such a case, for example, bottle 14 and bottle 20 would be the same with regards to their diamond pattern. The question to be answered, in short, is this: what does the diamond spacing mean?

I did some testing on a selection of ideas. My first idea was that the spacing simply described how many tubes each bottle is divided into. Our first bottle is a 1_4, so this idea would claim that one unit goes in one tube while the other four units go somewhere else. Presumably, this also suggests that the 1 unit will go in a farther left direction than the 4 units, based on their order on the label. This is all well and good, but following it through encountered a problem very early.

Looking at the scale in more detail, we are supposed to keep it balanced. To make the force calculations and referencing easier, I labeled each hook on the number line -13 to +13. The pipes are placed in specific spots on the scale, specifically at locations
[-13, -5, -2, 4, 8, 11].
This means the force that the bottles apply to the scale will always be in only these 6 locations. The weight can be placed on any hook, which you'd think makes things easier. Unfortunately, the weight is 2 units in size. Therefore, any force the weight provides to the scale will be an even number; an even number multiplied by any number always results in an even number. Therefore, to keep the scale balanced, we must ensure that the forces the filled tubes apply are even amounts as well: to balance an even force on one side requires an equal force placed on the other.
What does this mean?
It means, young padawan, that our bottles that have an odd number of diamonds must fill only tubes standing on even numbers. For example, if we take a 3-diamond bottle and fill the yellow tube at location -5, then that would be -15 units of pressure on the scale. We cannot put the weight anywhere on the scale to perfectly balance 15 units, because the hanging weight cannot provide an odd numbered amount of pressure.

Looking back at the first bottle, our 1_4 bottle, lets assume that we must follow the rules I stated above. The 1 unit must go into an even numbered tube [-2, 4, or 8]. The 4 units should go into any tube to the right of that [4, 8, or 11]. Unfortunately, this is already impossible - putting 4 units into the 4 spot is 16 units of pressure, plus the 26 units of pressure already on the right end = 42 units of pressure. The 1 remaining unit of liquid and the hanging weight can only provide 28 units of pressure combined at maximum, not enough to balance the scale.

That might have been a lot to process, so let's make this easier. We have weight already on the right end. We must put weight on the left end of the scale to balance it. Of course, pouring the first bottle's contents into a tube on the right end would only make things worse. We can't pour the first bottle into the odd-numbered tubes, either, because its force cannot be balanced by our even-numbered hanging weight. By process of elimination, we can only pour the bottle - all 5 units - into the green tube. Things begin to look better: 5 units * -2 distance from the center = -10 units of pressure, + 26 units from the right hand side = +16 units of pressure on the scale. To balance this evenly with an added -16 units of pressure, the weight must be placed on the -8 hook.

You might be thinking, "Great! We have a plan." Unfortunately, this plan doesn't continue very far. Long story short, we can't keep putting odd-numbered diamond bottles into even-numbered tubes, because we will end up favoring the green tube too much and cause it to overflow.

All of this means something is wrong somewhere. Whether it was my analysis of the scale, or my analysis of the diamonds, something is not matching up properly.

My most recent failed idea was ignoring the spaces between the diamonds. I interpreted instruction-2 a bit more literally, and thought maybe the hanging weight's current location was our clue for where to pour the next bottle. The fact that the weight is already hanging on the scale at the start of the puzzle gave the idea some credence, so I followed through. As before, we can't put only one unit nor all 5 units into the red pipe, as it would provide an odd pressure or too much pressure, respectively. The remaining option would be to put 4 units into the red and the remaining one elsewhere. This yielded multiple answers, somewhere around 9 different possibilities, but I remembered that this scenario has an additional rule: the hanging weight must be under a pipe so that we can identify where to pour the next bottle. There was only one solution that allowed this, which was pouring the last unit into the cyan tube and placing the hanging weight under the purple tube. This is where the idea fails, however, as we next have a 3-diamond bottle which is to be placed into the purple tube. 3*11 is 33, an odd pressure, and once again cannot be balanced by our even-sized hanging weight.

It seems this is the only remaining difficult point to reason out in the puzzle. I figure once we have a system that works without fail, it's just a matter of applying it to reach the answer. Almost certainly, the code will be broken by selecting the key related in color to the pipe that the bottle fills, selecting the line with the color that the hanging weight is beneath, and matching it with the same colored column as the key. For example, if the bottle fills the red pipe and we had to place the hanging weight on hook 4, then we'd insert the red key into the table, select the 4th row from the bottom (where the bright purple is), and select where it meets the red column on the same side, which happens to be the letter D. Noted, for this reasoning to be correct, it assumes that the whole of each bottle is poured into only one tube, which conflicts with most of my other reasoning above. I fear that I have overlooked something very basic and that all of my work and thinking has been flawed from the very beginning.

Original Post

I started into this puzzle today, hopefully I'll get to help you guys out solving this. I see you've made some good progress. I noticed something regarding the scale section, in that there were blank spots where there should be colors (like where the cyan tube ends). The keys offer a solution to this, since all the keys have the same color pairs, and those color pairs match up perfectly to their spacing on the scale.
I've taken the liberty of submitting a complete scale image:

More to do:

Let's take a look at the tubes. Those things are awkwardly shaped and must have a reason for it. I hypothesize that the tunnels are not actually in the right place. There's that weight on the right hand side; could it actually be a pipe with grey contents? If this is the case, then my hypothesize holds water (excuse the pun) - that is, we now have a correlation between the dots and the scale - 7 dots against 7 pipes. We would probably need to reorganize the pipes on the scale and see where the weight distributes itself when the pipes are full of a color.

My second hypothesis comes from looking more closely at the first instruction. It clearly shows the diamonds on the example bottle, so it's possible that it is giving us a clue about what the diamonds mean. From what it looks like, the diamonds are the amount of a color there is in the bottle, and it is pouring into a tube that already has contents. In this case, I suspect that the contents of the tubes persist, and our weight calculations will compound as we go through the bottles. We will be able to identify our mistakes by any tubes that are overfilled. Furthermore, there are times when we see up to three sets of diamonds on a bottle - this would indicate three different colors, if this hypothesis holds true, and we must compensate for that in our analysis.
*Note: I counted up the number of spaces in the tubes (95 empty) and the number of diamonds on all the bottles combined (93). Assuming I counted accurately, the fact that we can "fill the tubes with diamonds", so to speak, helps support the hypothesis that the diamonds represent the amount of something in each bottle.

• I think I reached a dead end. Seven bottles in, I reach a point where all lines fail. I will double check my 400 lines of notepad mathematics for somewhere I might have gone wrong, but I feel like I was being extra careful. Nevertheless, the longest path I have found is in the following order: Y->C->G->G->B->R->P. Please verify. – Bulldogg6404 Feb 17 '15 at 18:15
• 5Y; 3C; 7G; 2G; 4B; 3R; P4 seems to be correct in my book. Next is 4?; and this should be possible... – BmyGuest Feb 17 '15 at 19:28
• !!! I have to check at which point of copy-pasting the images that happened. It clearly is a mistake and I'll have to edit the images. (The image above was copy&pasted from the same Corel-file!)... – BmyGuest Feb 17 '15 at 21:02
• So far, now, the math and numbers have been lining up well enough. All I know is, being at bottle 18, I have five potential paths. I'm expecting this 'heavy' bottle to eliminate a few of the options. We will see. – Bulldogg6404 Feb 17 '15 at 21:48
• I believe there are two solutions to the /scales/, although it doesn't impact the puzzle at all, since the letters you get from them will be enough information to know if you have a valid sentence or not. I'm not quite at the end of the scale work yet, but I'm getting close, I believe. – Bulldogg6404 Feb 17 '15 at 22:58

We're down to the final part of the puzzle.
Note: this is the solution to the final instruction. Check the wiki for the first two parts.

Clearly, the scale work was the more difficult part. Now it should be smooth sailing. Our solutions to the first two parts are in the wiki, and I'll be making reference to those here.

The final instruction has four parts. The first two parts are relevant to selecting the key(s) we need, while the last two parts are the process of using the key(s) to get letters and put them into a sentence. There are a number of ways to go about this, but only one will be the right solution. It's just a matter of figuring out each part in detail.

Noting the final scale, we see that all of the tubes have been filled except one; the red tube is missing two units. The diamonds were our indicator for how many units filled the pipes, and there just happen to be two more diamonds on each of our keys. It seems quite obvious that this means we are supposed to use the red key in our solution, as the red key's two diamonds represent the missing two units on the final scale.

Side note: Does this change the weight on the balance? No, because adding two more red units is an additional 22 weight to the left side of the scale, which without the hanging weight's presence is a total of 34 weight on the left. The hanging weight would be unable to bring balance to the scale.

So, we have identified the use of the red key in finding our answer. Is it the only key we use? Yes, because the means of identifying the red key cannot be applied anymore to identify other keys. It is reasonable to believe that the red key is an anchor and will be used for the entirety of the final puzzle.

Is it an anagram? No, because the final instruction's last part shows that the letters are placed in order.

The hanging weight's position for each bottle is a clear indicator of which color - and in turn, the row - on the key we need to be looking at to determine the letters we need.
The original author says that the final solution will be an English sentence, so we will be able to check our progress along the way if we run into a selection of letters that does not make up an English word.

The only thing remaining is selecting a column. Presumably, the color of the pipe we filled with each bottle is how we should select our column. Following this line of thought, and knowing our first bottle goes into the yellow tube and the hanging weight balances at position +1, we find our first letter:

By continuing this process for each bottle, we find all of the letters in the final sentence. We discover that the / symbols are empty spaces. In summary, the combination of 1) the red key; 2) the row on the key corresponding to the hanging weight's position, and 3) the column of the color corresponding to the tube we fill with each bottle yields the following sentence:
BALANCE IS THE RECTIFIER

Excellent work, Bmyguest, this puzzle was certainly one of the most challenging and mentally-consuming puzzles I've had the pleasure of solving. Thanks to all the people who contributed their work, as well. It was fun! =)

• I like your logic. Are you sure about the first letter though? – BmyGuest Feb 18 '15 at 21:42
• What in the world...? Now I feel quite silly. – Bulldogg6404 Feb 18 '15 at 22:59
• Edited the post; now it's the solution to the 3rd instruction. – Bulldogg6404 Feb 18 '15 at 23:54
• Done and dusted :c) I will return later to "clean up" this thread with a final, all-inclusive answer for easier browsing. Short on time right now. – BmyGuest Feb 19 '15 at 11:06
• I did "un-accept" your answer because I felt I want the "complete" (wiki) answer to be the accepted one, so that later readers can easily first read "the whole puzzle" and then "the whole solution". However, I've started a bounty which I will award to this answer here tomorrow. (I have to wait 23 hrs) – BmyGuest Feb 20 '15 at 17:27

I found a sequence with all 24 bottles that works:

I then got the letters by taking the combination of tube color and weight color. The result makes no sense:

BTLFH/B/UTIUTX/UN/JIFIZE

• If you table your results, could you add one column with 'volume' for easier checking. And if you could use the colours instead/additionally to the pipe-numbers, it would be easier,too. i.e 1=R 2=Y 3=G 4=C 5=B 6=P (Forget my initial comment, I've misinterpreted your table. Still comparing...) – BmyGuest Feb 18 '15 at 18:10
• After careful checking I can confirm, you've found a correct solution for the balance puzzle. As a matter of fact, you've found one of two solutions, but the other only differs in a flip between bottle 11 and 15. The last part of the puzzle the key will easily help to discriminate between the two, but your first attempt was not successful... – BmyGuest Feb 18 '15 at 18:32
• Something to note: swapping the 11th and 15th bottles changes the hanging weight's placement in between those bottles, resulting in a section of letters being incorrect in the final answer. – Bulldogg6404 Feb 19 '15 at 0:00