Timeline for Sum and Product game
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| May 2, 2020 at 23:45 | comment | added | Thomas | Yeah that is a good description of it | |
| May 2, 2020 at 10:44 | comment | added | François Brunault | Sorry but I still don't get it. Do you mean to ask whether there exists at least one sequence of declarations which enables the logicians to find the numbers? | |
| May 2, 2020 at 10:41 | comment | added | Thomas | Okay, what I'm asking is this: Given the constraints of the problem, can the logicians figure out the numbers? No strategies, no coded information, only logic. | |
| May 2, 2020 at 10:29 | comment | added | François Brunault | Then I don't understand precisely your question "Is there always some strategy like this?". Do you mean to ask whether the logician S (or P) has a winning strategy regardless of what the other logician will say? That's different from finding a common strategy. | |
| May 2, 2020 at 10:22 | comment | added | Thomas | @FrançoisBrunault No, they have never met before. | |
| May 2, 2020 at 9:21 | comment | added | François Brunault | Are the logicians allowed to agree on a strategy before the conversation? | |
| May 1, 2020 at 23:26 | history | edited | Thomas | CC BY-SA 4.0 |
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| May 1, 2020 at 23:02 | history | edited | Thomas | CC BY-SA 4.0 |
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| May 1, 2020 at 5:08 | history | edited | Thomas | CC BY-SA 4.0 |
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| May 1, 2020 at 0:57 | history | edited | Thomas | CC BY-SA 4.0 |
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| May 1, 2020 at 0:18 | comment | added | Thomas | @JoshuaZ I think that is too strong of a limitation on the conversation. I'll edit my question to show what I mean, in particular, to show that even (3,4) is impossible to figure out using that method. | |
| May 1, 2020 at 0:18 | comment | added | Thomas | @FrançoisBrunault, with regards to state of knowledge. Let's say that the two logicians can only say things like "I know/don't know the numbers", and "I knew/didn't know what you just said before you said it". | |
| Apr 30, 2020 at 12:32 | comment | added | JoshuaZ | Let's restrict things a bit: Suppose they only keep saying "I don't know" until one of them finds out the numbers. Is there a number which we can construct where they'll never figure it out? My guess is that for any starting pair of positive integers, eventually they'll get it; this is based on the fact that products of two distinct primes have a pretty high density. | |
| Apr 30, 2020 at 10:07 | comment | added | François Brunault | So at the beginning the logicians only know that $x,y \in \mathbb{N}$? The solution to this puzzle depends strongly on the given domain of $x,y$. But here you're asking a different question, namely about the strategy of the logicians. However, how do you define "state of knowledge"? What is the difference with "information about the numbers themselves"? | |
| Apr 30, 2020 at 8:35 | comment | added | Thomas | Those seem to be about very specific cases, where there are restrictions on the sum, and the reader has to figure out the numbers. I'm asking if, given any two numbers, the logicians can figure it out. | |
| Apr 30, 2020 at 4:34 | history | edited | Thomas | CC BY-SA 4.0 |
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| Apr 30, 2020 at 4:12 | comment | added | Thomas | @LSpice, yes, positive integers | |
| Apr 30, 2020 at 4:07 | comment | added | Gerry Myerson | Much discussion at math.uni-bielefeld.de/~sillke/PUZZLES/sp.txt | |
| Apr 30, 2020 at 2:04 | comment | added | Max Alekseyev | See discussion at artofproblemsolving.com/community/c146h150971 | |
| Apr 30, 2020 at 0:10 | comment | added | LSpice | Presumably, the positive numbers are positive integers? | |
| Apr 29, 2020 at 22:04 | history | edited | Thomas | CC BY-SA 4.0 |
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| Apr 29, 2020 at 21:48 | history | asked | Thomas | CC BY-SA 4.0 |