3 ms·

Bonus meta-puzzle: the puzzle as stated is actually unsolvable. Both Sandy and Peter have to know something that the puzzle implies but does not actually stipu

by lisper 5y ago

Bonus meta-puzzle: the puzzle as stated is actually unsolvable. Both Sandy and Peter have to know something that the puzzle implies but does not actually stipulate that they know. What is it?

onionisafruit 5y ago
Is it that the other person was told either the sum or the product? Or that the number they were told is the sum or product? edit: After rereading the problem they weren’t told the parameters of the problem or even that they are participating in a puzzle.
- AveburySutton 5y ago
  process of elimination. as soon as peter starts, all primes are off the table. Given that, some number pairs which sum to the same number as just one other number pair where the second number pair has at least one prime are off the table. And so on and so forth. My instinct was to program the solution. Bet there are people who could do it in their heads.
  - caf 5y ago
    It's only the primes above 50 that are immediately eliminated by the fact that Peter does not know the answer right away. The primes below that can be present in products that have multiple possible answers: eg. we can't eliminate 47 right off the bat because Peter could have been told a product like 3290.
  - corndoge 5y ago
    >as soon as peter starts, all primes are off the table How do you figure? If Peter is given 97 (a prime), how is he supposed to know that a) he's been given a product (puzzle doesn't say he was told it's a product) and b) if he knows he's been given a product how is he supposed to know 97 is prime? He wasn't told that in the puzzle either.
nicoburns 5y ago
That the other person is following the same system as them to decide whether they "know the numbers". It would be super easy for one of them to say they don't know for some other reason, in which the others' reasoning would be false.
- mypastself 5y ago
  This is what I thought. Two unstated (but implied) parts of the puzzle are that they can’t tell each other the numbers outright, and that they can only share information in yes/no format. But since they have clearly already agreed on a system beforehand, they could have also encoded the digits in binary or something. So each person could have been sharing one binary digit of their number with each round. Or they might have used a completely different encoding. We simply cannot know.
ghayes 5y ago
That the order of the numbers is unimportant? Otherwise every non-duplicate solution has a correlate solution, inverted. E.g. (3,2) implies (2,3) is also a solution.
- onionisafruit 5y ago
  I don’t think that’s necessary. The problem only says there are two numbers, not that the numbers have any order.
taormina 5y ago
The number of steps it would take to solve the puzzle.
- thaumasiotes 5y ago
  No, they discover that as they talk. It's not something they need to know; it's something you need to know.
arjvik 5y ago
That both are perfect logicians with an understanding of the system sans the information about the two numbers themselves?
- hackernewds 5y ago
  since this is a fair assumption (that they will humanly miss a combination when true) the next inference is they have access to a perfect calculator
cortesoft 5y ago
They both have to know what the other person knows (e.g the product or sum), and that the other person is a perfect logician.
joemi 5y ago
The fact that it's unsolvable as stated is precisely why I hate this puzzle.
Sankozi 5y ago
Each one of them: 1. is a person that solves logical puzzles if possible 2. knows that the other one + (insert point 1 here). 3. knows that the other one + (2) 4. knows that the other one + (3) ...
- drexlspivey 5y ago
  This is called Common Knowledge in game theory: Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as {\displaystyle C_{G}p}.
deleted 5y ago
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by lisper 5y ago

Bonus meta-puzzle: the puzzle as stated is actually unsolvable. Both Sandy and Peter have to know something that the puzzle implies but does not actually stipulate that they know. What is it?

onionisafruit 5y ago

Is it that the other person was told either the sum or the product? Or that the number they were told is the sum or product? edit: After rereading the problem they weren’t told the parameters of the problem or even that they are participating in a puzzle.

AveburySutton 5y ago
process of elimination. as soon as peter starts, all primes are off the table. Given that, some number pairs which sum to the same number as just one other number pair where the second number pair has at least one prime are off the table. And so on and so forth. My instinct was to program the solution. Bet there are people who could do it in their heads.
- caf 5y ago
  It's only the primes above 50 that are immediately eliminated by the fact that Peter does not know the answer right away. The primes below that can be present in products that have multiple possible answers: eg. we can't eliminate 47 right off the bat because Peter could have been told a product like 3290.
- corndoge 5y ago
  >as soon as peter starts, all primes are off the table How do you figure? If Peter is given 97 (a prime), how is he supposed to know that a) he's been given a product (puzzle doesn't say he was told it's a product) and b) if he knows he's been given a product how is he supposed to know 97 is prime? He wasn't told that in the puzzle either.

nicoburns 5y ago

That the other person is following the same system as them to decide whether they "know the numbers". It would be super easy for one of them to say they don't know for some other reason, in which the others' reasoning would be false.

mypastself 5y ago
This is what I thought. Two unstated (but implied) parts of the puzzle are that they can’t tell each other the numbers outright, and that they can only share information in yes/no format. But since they have clearly already agreed on a system beforehand, they could have also encoded the digits in binary or something. So each person could have been sharing one binary digit of their number with each round. Or they might have used a completely different encoding. We simply cannot know.

ghayes 5y ago

That the order of the numbers is unimportant? Otherwise every non-duplicate solution has a correlate solution, inverted. E.g. (3,2) implies (2,3) is also a solution.

onionisafruit 5y ago
I don’t think that’s necessary. The problem only says there are two numbers, not that the numbers have any order.

taormina 5y ago

The number of steps it would take to solve the puzzle.

thaumasiotes 5y ago
No, they discover that as they talk. It's not something they need to know; it's something you need to know.

arjvik 5y ago

That both are perfect logicians with an understanding of the system sans the information about the two numbers themselves?

hackernewds 5y ago
since this is a fair assumption (that they will humanly miss a combination when true) the next inference is they have access to a perfect calculator

cortesoft 5y ago

They both have to know what the other person knows (e.g the product or sum), and that the other person is a perfect logician.

joemi 5y ago

The fact that it's unsolvable as stated is precisely why I hate this puzzle.

Sankozi 5y ago

Each one of them: 1. is a person that solves logical puzzles if possible 2. knows that the other one + (insert point 1 here). 3. knows that the other one + (2) 4. knows that the other one + (3) ...

drexlspivey 5y ago
This is called Common Knowledge in game theory: Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as {\displaystyle C_{G}p}.

deleted 5y ago

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