[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 442
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73 does not fit. If this number had been communicated to Sage B as a sum, he, having no information, could not deny the combination of 2 and 71, i.e. the one-digit decomposition of 2*71 = 142 into multipliers. 71 is prime.
Your paraphrase of phrase B is not entirely accurate.
Lemma. For B to say his phrase "I knew without you that you wouldn't find a number", n. and e. that the sum communicated to him must be less than 100 and be represented as 2+complete_odd.
Try proving it.
I'm off to bed.
Hello, everyone! I've been listening to a lot of you!
Can we move on from the reasoning to the programming?
Can someone write a script that goes through all the options and rejects the ones that don't fit the conditions?
Can someone write a script that goes through all the options and rejects the ones that don't fit the conditions?
So there is no way to do it without combinatorics?
In order to program, you have to have a clear idea of what information the wise men pass to each other during the exchange of replicas. The first three lines are clear, but the information received by B after the third line is not quite clear to me. More like "not quite got it"...
What kind of information does B get from A after the third line?
What kind of information does B get from A after the third line?
point 4 of my reasoning
So you can't do it without combinatorics?
In my opinion, it is enough to do with simple brute force, which requires, as Mathemat pointed out, translating the words of the Wise Men into a more comprehensible language of letters.
Can it be posted already? ))
Expression one:
Original: I can't define numbers.
Positively: A given product can be obtained in more than one
in more than one way.
Action: remove pairs of numbers whose product can be obtained
in a single way:
It is clear that par. 4. The most important thing is to formalize it.
Let's formalise it.
With the third remark ("Then I know the numbers") A informed B that the information in B's remark "I knew in advance that you could not determine the numbers" was enough to solve the problem.
This was enough for B to solve it, too.
--
Is that clearer? I didn't say anything new, I just spelled out the content of the messages.