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“I don't know the numbers”: a math puzzle

alexanderell.is

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Re: “I don't know the numbers”: a math puzzle

#111

Post by 6gvONxR4sf7o »

My favorite version of this is a real mind fuck.

http://jdh.hamkins.org/cheryls-rational-gifts/

Two people are told rational numbers of a particular form. They want to know whose number is larger:

> Albert I don’t know.

> Bernard Neither do I.

> Albert Indeed, I still do not know.

> Bernard And still neither do I.

> Cheryl Well, it is no use to continue that way! I can tell you that no matter how long you continue that back-and-forth, you shall not come to know who has the larger number.

> Albert What interesting new information! But alas, I still do not know whose number is larger.

They keep saying “No matter how much we do this, we still won’t know” and eventually they know. It’s great and I recommend reading it.

Re: “I don't know the numbers”: a math puzzle

#112

Post by kgwgk »

Forgeties79 wrote: post #106
kgwgk wrote: post #72

Earlier quoted context omitted.

Nature doesn’t chase anything. Things happen. Arguably surviving may happen less often for the shock-proof egg than for the egg that is better in some alternative aspect (including quantity). (Maybe the hard egg has other advantages though. Could also be used to produce a better skeleton.)

That’s exactly what I said. “Selects out” is the terminology used when discussing evolution. It’s not an active “decision,” it’s a thing that happens. “Natural selection.”

Ok. But what does that mean in the context of the comment that you replied to? (Which doesn’t talk about decisions or nature chasing things, at least as it stands now.)

Is a harder shell which has higher costs than benefits selected out? Maybe we’re all repeating the same thing.

Re: “I don't know the numbers”: a math puzzle

#113

Post by Someone »

drexlspivey wrote: post #97
Someone wrote: post #56

Earlier quoted context omitted.

The ‘normal’ way to write something like that (I hope I got the range ends right) is for i in range(1, N): for j in range(1, j + 1): candidate_pairs.add((i, j)) Also, conceptually, you don’t have tuples, but multisets. If you were to use those, you wouldn’t need that if at all. Multiset isn’t built-in to python, so you’d need to use an external package. Alternatively, write a class for storing pairs of ints i , j tha…

Python actually has built in support for multisets, you use a set of frozensets >>> a = set( (frozenset((1,2)), frozenset((3,4)) ) ) >>> frozenset((2,1)) in a True

That’s not a multiset, it’s a set containing tuples. A multiset (https://en.wikipedia.org/wiki/Multiset) allows you to add identical items multiple times.

You would use that to, for example, store the knowledge that 6 can be written as 3+3, by using a multiset {3,3} instead of a tuple (3,3)

Re: “I don't know the numbers”: a math puzzle

#115

Post by robocat »

the_af wrote: post #103
kgwgk wrote: post #72

Earlier quoted context omitted.

Nature doesn’t chase anything. Things happen. Arguably surviving may happen less often for the shock-proof egg than for the egg that is better in some alternative aspect (including quantity). (Maybe the hard egg has other advantages though. Could also be used to produce a better skeleton.)

I would understand the selective advantage if it made the egg shell more resistant to accidental breaking within the nest. But for birds that nest in tree branches or perches, what advantage is there for an egg resisting a fall without breaking? That egg is lost anyway; for most bird and egg shapes, there's no way to bring it back to the nest.

https://www.theatlantic.com/science/archive/2017/06/why-are-...

Off topic, but indirectly supports your point.

Re: “I don't know the numbers”: a math puzzle

#116

Post by hamburglar »

Layke1123 wrote: post #65
hamburglar wrote: post #61

Earlier quoted context omitted.

I’m not one of the downvoters but I suspect he’s being downvoted for an inability (or refusal) to think in hypotheticals for the sake of an interesting problem. It gives the impression of someone who so dislikes thought exercises or is too insecure about their ability to solve them that they prefer to ruin them with silly objections about practicality.

No, what I think he is highlighting is how people not interested in math approach a problem like this. I asked my girl friend this question on the way home from our Mother's Day dinner, and she had a very similar statement. It says something about how mathematicians could improve on their analogies, not whether he is interested in solving a math problem. I found it insightful even if it was not directly tied to the "…

It doesn’t really have anything to do with math. It’s problem solving. I’m pretty sure the legendary farmer who had to get his fox and chicken across the river never actually existed, but the point of the problem is to be a framework for using your brain, not an actual attempt to help a farmer with a real dilemma.

Maybe someone doesn’t enjoy these types of problems, but objecting based on the obviously-contrived premise not being realistic just makes them look dumb.

Re: “I don't know the numbers”: a math puzzle

#117

Post by Forgeties79 »

kgwgk wrote: post #112
Forgeties79 wrote: post #106

Earlier quoted context omitted.

That’s exactly what I said. “Selects out” is the terminology used when discussing evolution. It’s not an active “decision,” it’s a thing that happens. “Natural selection.”

Ok. But what does that mean in the context of the comment that you replied to? (Which doesn’t talk about decisions or nature chasing things, at least as it stands now.) Is a harder shell which has higher costs than benefits selected out? Maybe we’re all repeating the same thing.

Ah I get what you’re saying. My point is that yes, some other type of shell probably selected out and this one wasn’t. Maybe it was dumb luck, maybe it was a slight advantage in a very specific condition that allowed it to persist, but ultimately we can only theorize.

Re: “I don't know the numbers”: a math puzzle

#118

Post by caf »

vintermann wrote: post #100
refurb wrote: post #99

Earlier quoted context omitted.

I would assume it hinges on the fact that when one party says "I don't know the answer" then they are eliminating a possibility (which isn't intuitive at all with that answer).

I believe (I could be wrong here, I haven't rigorously checked this) that when the numbers are less than 100 and both parties know this, there will always be a possibility eliminated by a "I don't know" statement.

After the round in the posed problem, it reaches a stalemate.

If Peter had said "I don't know the numbers" at the end there, Sandy can exclude the possibility that the numbers were 77 and 84. However, at this point Peter already knows that Sandy still doesn't know the numbers: Even if the sum Sandy was told was 161, there are still five remaining live possibilities for that sum (62 + 99, 65 + 96, 70 + 91, 76 + 85 and 80 + 81), so Peter gains no new information from Sandy's next statement that Sandy does not know the numbers.

Re: “I don't know the numbers”: a math puzzle

#119

Post by caf »

AveburySutton wrote: post #31
onionisafruit wrote: post #4

Earlier quoted context omitted.

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.

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.

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.

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