Ridiculous Parlor Room puzzle

[Parmanello]

Blue box - "you will not solve this puzzle"

White box - "four statements on boxes in this room are true" and "a box with one false statement contains the gems"

Black box - "a box with true statements contains the gems" and "this box does not contain the gems".

The blue box clue was throwing me because if it's not true or false until I attempt to open a box and my choice is either correct or not. So if I understand the game correctly the options are

Blue T, W - T T , B - F F - Invalid as 4 statements aren't true
Blue T W - T F, B - F F - Invalid as 4 statements aren't true
Blue T, W - F T, Black - F F - Invalid as white and black implied to contain gems
Blue T, W - F F, Black - F T - implies white, but if I solve it then blue is F so this is invalid
Blue T, W - F F, Black - T F - as above if there's a solution blue can't be true as I'd have solved the puzzle
Blue T, W - F F, Black - T T - as above if there's a solution blue can't be true as I'd have solved the puzzle
Blue F, W - F F, Black - T T - invalid as black contradicts itself
Blue F, W - T F, Black - T T - invalid as only 3 true statements
Blue F, W - F T, Black - T T - White implied
Blue F, W - T T, Black T T - not checking as white is solution
Blue F, W - T T, Black F F - not checking as white is solution
Blue F, W - T T, Black T F- not checking as white is solution
Blue F, W - T T, Black F T- not checking as white is solution

So I chose white and it contained the gems (mercifully). But at this point I am so tired of doing these lengthy logic checks to get 3 gems. The gems are important though so every run needs to have a parlor game win. Any way to alleviate this slog would be appreciated.

[rumpelstiltskin]

i think blue is false, since all puzzles are supposed to be solvable, you'd have to assume you'll solve this one as well.
and yes there's a way to alleviate the slog - https://www.nexusmods.com/blueprince/mods/3?tab=files

[Forblaze]

blue - We know this is false because you're a smart boy and we believe in you. There are a few cheeky statements and this is really the only logic you need to figure them out.

white -
We know the four statements being true statement is false because then both white and blue are entirely true.

"This box contains the gems" could be true or false. We aren't sure.

Black - we already have the false box accounted for and we know white isn't entirely true, so we know this has to be the true box.

A box with a true statement contains the gems - if white contains the gems, this is true.

this box does not contain the gems - therefor it has to be another box.

So going back to the white box, we can deduce that the second statement is true.

[TroeLar]

I've just stumbled on this particular puzzle, and I think the rules of the game make this - and perhaps other - impossible?

Now I could be missing some additional rules added in some other room or puzzle, but going by the papers in the room this puzzle would seem to contradict them.

The rules specifically say that:

There will always be at least one box which displays only true statements.
There will always be at least one box which displays only false statements.

The key word being 'only'.

If those rules are not modified elsewhere, then assuming blue is false (and thus we have at least one box containing only false statements), either white or black must contain ONLY true statements.

As black contradicts itself it does not contain only true statements, so white must contain only true statements.

But given that black must contain one false statement and blue is false, then the statement on the white box, that there are four true statements is false, meaning that white does not only contain true statements.

The puzzle therefore does not contain a box which displays only true statements.

I am guessing the rules should actually be interpreted as there will always be at least one true statement and one false statement, but that is specifically not what is given on the papers.

[Silyon]

Originally posted by TroeLar:

As black contradicts itself it does not contain only true statements, so white must contain only true statements.

This part is the error in that logic, and is due to reading comprehension. The first statement on the black box says "a box with true statements contains the gems", which can be any box with a true statement and not necessarily the completely true box. No contradiction.

[Gorlom[Swe]]

White box - "four statements on boxes in this room are true" and "a box with one false statement contains the gems"

Blue T, W - F T, Black - F F - Invalid as white and black implied to contain gems
Blue T, W - F F, Black - F T - implies white, but if I solve it then blue is F so this is invalid

I'd say this is incorrect. in the top one Black has two false statements, not one. This implies white holds the gems, but then violates Blue being True, as you point out on the second one. Edit: Wait. it does imply both as Black 2 would be false. So there is a contradiction where 2 boxes claim the gems through different statements.
The second one however has two false statements on white and would not imply white. Edit: but also would prevent black as B2 would be true.

Edit: hmmm. I overlooked B2

[TroeLar]

Originally posted by Silyon:

Originally posted by TroeLar:

As black contradicts itself it does not contain only true statements, so white must contain only true statements.

This part is the error in that logic, and is due to reading comprehension. The first statement on the black box says "a box with true statements contains the gems", which can be any box with a true statement and not necessarily the completely true box. No contradiction.

I think I take your point, but I don't think the puzzle obeys the rules even so. And this will be nitpicking on language.

Black statements are:

B1 "a box with true statements contains the gems"
B2 "this box does not contain the gems".

And white has:

W1 "four statements on boxes in this room are true"
W2 "a box with one false statement contains the gems"

Black cannot have the gems. IF black had the gems, then this causes B1 and B2 to clash, so white must display only true statements.
But if either B1 or B2 is false, then W1 is false, and no box displays only true statements.


White, however, also cannot have the gems.

B2 is true because white has the gems.
B1 states that a box with true statementS contains the gems.
So for black to display only true statements, then white must also display only true statements.
If either W1 or W2 is false, then so is B2 and the rules are not obeyed, because no box displays only true statements.

But, if both W1 and W2 are true, then W2 is false since the the box with the gems does not have a false statement.
In turn B1 is false, since the gems are in a box that does not contain multiple true statements.

Whether black or white has the gems, there is not box displaying only true statements.

EDIT:
I feel I should add, that while we could perhaps read B1 as a way of saying only 1 true statement is required, then W2 shows that the game can differ between one and multiple statements.

[Mercurial]

This sounds like OP falsely copied "a box with a true statement" as "a box with true statements".

If the actual game said statements, plural, it's logically inconsistent.

If the actual game said statement, singular, then Blue is All False and Black is All True and White is False-True and contains the gems.

[TroeLar]

Originally posted by Mercurial:

This sounds like OP falsely copied "a box with a true statement" as "a box with true statements".

If the actual game said statements, plural, it's logically inconsistent.

If the actual game said statement, singular, then Blue is All False and Black is All True and White is False-True and contains the gems.

That's a good point. I've gone beyond it now, but I looked up elsewhere, and someone had it singular. So I guess all my ranting is moot.

Thanks all and carry on.

[jlyles717]

Just got this puzzle with a friend and got it wrong (almost intentionally). I ended up guessing the blue box because I had to know if it was some sort of trick lol. But at the beginning we thought maybe the blue box could be some sort of "Schroedinger's box". Where it is both true AND false, leaving the other two to be either true or false instead of the possibility of both being true or false.
Does that make any of the logic possibly make more sense to you guys? Either way, no gems for me and I'm moving on. My head hurts...

[kory]

Originally posted by jlyles717:

Just got this puzzle with a friend and got it wrong (almost intentionally). I ended up guessing the blue box because I had to know if it was some sort of trick lol. But at the beginning we thought maybe the blue box could be some sort of "Schroedinger's box". Where it is both true AND false, leaving the other two to be either true or false instead of the possibility of both being true or false.
Does that make any of the logic possibly make more sense to you guys? Either way, no gems for me and I'm moving on. My head hurts...

Even if Blue is somehow true and false, that doesnt mean it has gems, your goal is not to find a true box, your goal is to find the gems.