I present to you two baskets, with lids closed. Both of the baskets have notes attached to them.
On basket 1 is written,
“Either this basket contains nothing, or the basket with the false note contains nothing, but not both.”
On basket 2 is written,
“Either this basket contains $1million and the basket with the false note contains nothing, or this box contains nothing and the box with the true note contains $1million.”
One note is true, and one note is false. One basket contains $1million, and one contains nothing. I will give a picture of $1million to the the first one to both answer correctly and tell me how they proved it. Let the race begin!
I must also assure you that there’s no word game going on here, and the answer is deducable.
Note two is true. If note one is false, it doesn’t have to adhere to its rule. All other explanations end in paradox. Do I need to clarify further, or does that suffice?
if you are right, you’ll have to give a bit more of an in depth explanation than that. gotta prove it brah. and i won’t be giving you any hints on how. i also refuse to tell you if you are right until you prove it.
i’m like ur highschool math teacher: gotta show your work. otherwise you could just be accidentally correct.
If basket one contains nothing because the note is true, then it is impossible for the other basket to contain nothing by default as it clearly states that both cannot contain nothing. But as the rule states the basket with the false note contains nothing, it is non sequitur that the note can be both true and false.
If the second basket (purportedly containing one million) is true, then it does follow that the first note is false. If the second note is false, it is non sequitur that note one could be true and false simultaneously (as the note indicates it contains nothing, it could not be true and contain one million).
You have two options for basket one:
a) This basket contains nothing.
b) The basket with the false note contains nothing.
You have two options for basket two:
a) This basket contains $1million and the basket with the false note contains nothing.
b) This box contains nothing and the box with the true note contains $1million.
Further, you specify “One note is true, and one note is false. One basket contains $1million, and one contains nothing.” We’ll designate this “R”.
So if 1a is true, R dictates that 1b is false.
1b is true by default.
If 2a is true, note one is false and R is satisfied.
If 2b is true (thus 1a is true), R is not satisfied.
Assume B1 is true:
Note 1 says either B1 is empty and B2 is $ or B2 is empty and B1 is $ - logically ok
Test if B2 being false makes sense:
Note 2 says either B2 is $ and B2 is empty - always false which is ok
or B2 is empty and B1 is $ - that is only false if the money is in B2
Could B2 be true instead?
Note 2 says B2 is $ and B1 is empty or B2 is empty and B2 is $ - already inconstant on second part
Test if B1 being false makes sense:
Note 1 says B1 is empty - only false if money is in B1
or B1 is empty - only false if money is in B1
They can’t both be the same statement so B2 being true and B1 being false doesn’t make sense.
Then it is basket two.
Note one is true and note two is false.
2a contradicts 1a. (If 2a is true, 1a is true and 1b agrees with 2a, therefor note 1 is not false)
2b contradicts itself. (If basket 2 contains nothing, 2b is true and therefor should contain the money)
1b contradicts itself. (If 1b is true, note 1 must be true and therefor should contain the money, making 2b true)
1a is true. (If 1a is true, neither 1b nor note 2 can be true, so by R, the money must be in basket 2)
1a is true and the money is in the basket with the false note.
I’ve only read the opening post of this thread. I say the note on basket 1 is the false note. What’s false about it is that that basket is the basket with the false note, so that basket and the basket with the false note do both contain nothing. The note written on basket 2, then, is true: for though it does not contain nothing, it does contain $1 million and the basket with the false note contains nothing.
Basket 1 has the false note and contains nothing. It contains nothing and is has the false note, making both parts of the disjunction true (which its note says aren’t both true).
Basket 2 has the true note and contains $1 million. The note is a simple disjunction, and when one part of a disjunction is true (‘x’ or ‘y’) the whole statement is true. ‘X’ = ‘this basket contains $1 million and the basket with the false note contains nothing’ and is true, while ‘Y’ = ‘this box contains nothing and the box with the true note contains $1 million’ and is false because this box does not contain nothing. Since at least ‘X’ is true, though, the disjunction is true, thus the note is true.
Sauwelios and I are right. Note 1 says both parts of its disjunction cannot be true, but the both are: the basket contains nothing and it has the false note.
Let me try to be more clear. With the conditions of the puzzle in mind (one note must be false and one must be true, one basket must contain $1 million and the other nothing), basket 1’s note is self-contradictory. For its note to be true, one part of the disjunction has to be true. If either part is true, though, then both parts are true. But it says both can’t be true, from which it follows that neither can be true. So note 1 is false, which means note 2 has to be true.