PKM- Rigorous solution of the statue puzzle

[Trashos]

I am reposting here the rigorous solution to the (optional) statue puzzle which can be found in the beginning of PKM. The puzzle involves 6 statues with the sword up or down, and 6 buttons that switch the position of certain swords each. One treasure room opens when all swords point up, and another treasure room opens when all swords point down.

You can probably solve this puzzle eventually by randomly clicking on buttons, but here I am presenting the rigorous solution.

Note that if you want to develop your IQ or properly maintain an aging brain, puzzles such as this are excellent training. They are even worth studying, if you are serious about it.

The method in a nutshell:
1) Note initial condition of statues (up or down).
2) Try the buttons and write down which statues each button affects.
3) Find a succession of buttons (order does not matter) that affects the statues that need to end up changed an odd (1,3,5...) amount of times, and the statues that need to end up unchanged an even (0,2,4...) amount of times.

By affecting a sword an odd amount of times, you change its direction. If you affect it an even amount of times, it remains unchanged or returns to its initial direction after a small trip.

I am going to name the 6 statues s1-s2-s3-s4-s5-s6 and the 6 buttons b1-b2-b3-b4-b5-b6. Numbering starts in the first room you see, north. Numbering ends in the second room you see, south.

Step 1: Note initial condition of statues (up or down).

Spoiler

Spoiler

s3 ^ s1 ^
s4 v s2 v
s5 ^
s6 v

s1: up
s2: down
s3: up
s4: down
s5: up
s6: down

Therefore, we need to find the combination that changes s2, s4, s6 to unlock the first treasure, and then we need to find the combination that changes all statues to unlock the second treasure.

Step 2: Try the buttons and write down which statues each button affects.
(don't forget to press the buttons a second time to return the statues to their initial condition)

Spoiler

b1 affects s1, s2, s4
b2 affects s1, s2, s3
b3 affects s2, s3, s6
b4 affects s1, s4
b5 affects s5, s6
b6 affects s3, s5, s6

Step 3) Find a succession of buttons (order does not matter) that affects the statues that need to end up changed an odd (1,3,5...) amount of times, and the statues that need to end up unchanged an even (0,2,4...) amount of times.

Spoiler

The combination that points everything up and unlocks the first room is: b1/b2/b3. Why:
s1: affected 2 times (even). UNCHANGED.
s2: affected 3 times (odd). CHANGED.
s3: affected 2 times (even). UNCHANGED.
s4: affected 1 time (odd). CHANGED.
s5: affected 0 times (even). UNCHANGED.
s6: affected 1 time (odd). CHANGED.

Thus by pressing b1/b2/b3 all swords point up, and the first treasure room is opened.

AFTER THAT, we need to switch all swords to pointing down to unlock the other treasure room. The combination which achieves this is: b1/b6. Why:
s1: affected 1 time (odd). CHANGED.
s2: affected 1 time (odd). CHANGED.
s3: affected 1 time (odd). CHANGED.
s4: affected 1 time (odd). CHANGED.
s5: affected 1 time (odd). CHANGED.
s6: affected 1 time (odd). CHANGED.

Thus you have solved the puzzle!

A post will follow that will give an even more rigorous solution for Step 3.

 

[Trashos]

ALTERNATIVE STEP 3

The REAL rigorous solution involves a different strategy for Step 3, one that is a bit slower. For each statue, we will find the combination that changes it independently, while keeping everything else unchanged. Once we have the combination for each statue independently, we can basically do whatever we want at will.

Spoiler

First we figure out the easy statues, s2 and s3:

S2: b1, b4 (only s2 is affected an odd amount of times)

S3: b5, b6 (only s3 is affected an odd amount of times)

Now we can move on to the tougher statues:

S1: b2, (b1, b4), (b5, b6)

b2 switches s1, s2, s3. Then we press the combination that only switches s2 as mentioned above (b1, b4). then we press the combination that switches s3 as mentioned above (b5, b6). Therefore, at the end only s1 will be switched.

By the same logic, we continue with the rest of the statues:

S4: b4, (b2, b1, b4, b5, b6)

b4 switches s1 & s4. The rest of the buttons are the combination that switches s1 back, as mentioned above.

S5: b3, b6, b1, b4

The combination b3, b6 switches s2 & s5. Then the combination b1, b4 switches s2 back, as mentioned above.

S6: b5, (b3, b6, b1, b4)

b5 switches s5 & s6. Then the combination b3, b6, b1, b4 switches s5 back, as mentioned above.

 

[FriendlyMerchant]

That's a lot of work. I just click on things at random until everything works. Then repeat.

 

[Fowyr]

I always thought that game abbreviated as P:K.
PKM brings to my mind only this:

 

[CaesarCzech]

That's a lot of work. I just click on things at random until everything works. Then repeat.

Year later to shitpost, i just looked at what affected what and followed logic

 

[Sarathiour]

One treasure room opens when all swords point up, and another treasure room opens when all swords point down.

WAIT

THEY WERE TWO TREASURE ROOM ?

 

[aweigh]

Note that if you want to develop your IQ or properly maintain an aging brain, puzzles such as this are excellent training. They are even worth studying, if you are serious about it.

I just do CAPTCHAs

 

[Darth Canoli]

One treasure room opens when all swords point up, and another treasure room opens when all swords point down.

WAIT

THEY WERE TWO TREASURE ROOM ?

Aaaaaaargh!
I missed one as well, i have to reinstall the game at once and... Oh, nevermind, i just remembered how boring it is to play PK, i'm never installing this game again.

 

[EdgyRightWinger]

While OP is correct, he still deserves this reaction