Sunday, 22 December 2013

logical deduction - 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.







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.)









INSTRUCTION1



(Instruction 1)



INSTRUCTION2



(Instruction 2)



INSTRUCTION3




(Instruction 3)





BOTTLES



(The bottles)




SCALE


(The scale)






CODE



(The code)





KEYS



(The keys)







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



LABELS



(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.






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!




Answer




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)








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:
Dot-Labels in correct order

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"):

Scale-balance-example



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:

24-Solution-Steps

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:
Scales with colours completed
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:



NumberedScale with filled colors
solution positions



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:
RedKeyInSolution



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




BALANCE/IS/THE/RECTIFIER



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