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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

#101

Post by bertil »

tobr wrote: post #89

I understand it’s a puzzle and it requires some suspension of disbelief, but I think Peter is wrong. He doesn’t know the numbers after 14 tries. He is assuming that Sandy has figured out the trick and is able to correctly keep track of 9801 + 198 = 9999 lists of number pairs in her head. As far as I can tell by how the puzzle is phrased, that’s a totally unreasonable assumption. It’s more likely that she says “I don’…

It’s generally presented as both of them being experienced mathematicians who have been doing it for a while, that they have access to a notebook and a calculator and recently (I’ve seen those since the 1980s) to a computer.

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

#102

Post by bertil »

kthejoker2 wrote: post #63

A similar (simpler) well known puzzle > A census taker approaches a woman leaning on her gate and asks about her children. She says, "I have three children and the product of their ages is seventy–two. The sum of their ages is the number on this gate." The census taker does some calculation and claims not to have enough information. The woman enters her house, but before slamming the door tells the census taker, "I h…

There’s actually many variation of those Peter and Simon/Sally problems. I’ve seen with two, three and up to four numbers. Often, one of them claim they (finally) know the answer after a certain number of interactions and _then_ the other claiming that they either can, or can’t figure it out. “I knew that” or “Oh, really?” respond the one who knows, and finally: “Then I know what those are.”

One can include certain clues, like “Those are three beautiful numbers” to indicate those are different, or “You would like them” if either of them is presented as a fan of prime numbers, perfect numbers or something like that. With children’s age, they might be in school, boarding school, went to university, or have children, to indicate they are below or above 6, 14, 18, etc.

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

#103

Post by the_af »

kgwgk wrote: post #72
Forgeties79 wrote: post #49

Earlier quoted context omitted.

Nature doesn’t chase the better option. It selects out the options that aren’t good enough to survive.

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.

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

#104

Post by Layke1123 »

4ad wrote: post #80
Layke1123 wrote: post #65

Earlier quoted context omitted.

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 "…

One's disinterest or inability to do math has no bearing on the quality of a math problem.

That's not what this is about though. It's about sparking interest in math, and many on here are showing exactly why math people can me off putting for non math people.

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

#105

Post by SamBam »

cedilla wrote: post #77
PebblesRox wrote: post #62

Earlier quoted context omitted.

The puzzle is a good example of pseudocontext: "Instead of giving students realistic situations that they could analyze, textbook authors began to fill books with make-believe contexts – contexts that students were meant to believe but for which they should not use any of their real-world knowledge."[0] I think for a math puzzle that people choose to do for fun, pseudocontext is fine. We can suspend our disbelief and…

I'm not convinced by the pseudocontext critique. For one, I think the egg experiment is already sufficiently fantastical and its rules follow logically. Ignoring common sense reasoning is an important skill. We need rigorous answers where they are available, and the common sense answer is almost always very wrong. I still agree that school textbooks take this much too far in many cases, but this riddle is fine.

Except that I think it penalizes the neuro-diverse mind that can't get over the fact that this puzzle doesn't make rational sense, and they get stuck on that, at the expense of doing the problem.

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

#106

Post by Forgeties79 »

kgwgk wrote: post #72
Forgeties79 wrote: post #49

Earlier quoted context omitted.

Nature doesn’t chase the better option. It selects out the options that aren’t good enough to survive.

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.”

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

#107

Post by Forgeties79 »

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.

> what advantage is there

So this is a pretty common mistake people make when discussing evolution. It’s not about what is advantageous, it’s about what survives the selection process. A combination of odds that play out.

Our eyes are not advantageous or chosen by evolution, our eyes were just acceptable enough for us to survive while other variations were not. There was no decision or work/progress towards an end goal. A creature developed along a certain line by chance, the situation in nature was such that they survived and passed on that trait, while others did not. Natural selection in action.

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

#108

Post by 613style »

edflsafoiewq wrote: post #68
613style wrote: post #57

Earlier quoted context omitted.

I was asked this one in a google phone interview in ~2009. I remember deriving that intervals of 10 floors were optimal in the two-egg 100-story case using some simple calculus and getting that far took me most of the hour. Your solution is super nice, but I hope you don't ask candidates to recreate it :P

That's not optimal though, like the blog says. When doing the first egg, as you get up near the top you've already used up many drops, so the gaps need to get correspondingly smaller.

Maybe that's why I don't work at google :)

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

#109

Post by the_af »

Forgeties79 wrote: post #107
the_af wrote: post #103

Earlier quoted context omitted.

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.

> what advantage is there So this is a pretty common mistake people make when discussing evolution. It’s not about what is advantageous, it’s about what survives the selection process. A combination of odds that play out. Our eyes are not advantageous or chosen by evolution, our eyes were just acceptable enough for us to survive while other variations were not. There was no decision or work/progress towards an end go…

No, I understand how natural selection works. I'm a fan of Stephen Jay Gould.

Please keep in mind the original comment I was responding to:

> Eggs are evolutionarily designed to survive falling out of nests and perches.

My response is "no, they are not". First, like you said, they are not "designed" in any way. But that's the pedantic response. Second, there's no selective pressure for eggs resistant to dropping from a nest, since they are lost anyway and won't pass any genes. It's likely that something else is being selected for -- or at least, that the more resistant shell is not harmful to reproduction of the species -- but there's no selection for nest-drop-resistant eggs because that confers no advantage. Maybe it's just harmless, which can make the trait survive. See the difference?

> There was no decision or work/progress towards an end goal.

It helps to assume everyone understands this, otherwise we cannot get to the meat of the discussion without nitpicking every single sentence.

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

#110

Post by Forgeties79 »

the_af wrote: post #109
Forgeties79 wrote: post #107

Earlier quoted context omitted.

> what advantage is there So this is a pretty common mistake people make when discussing evolution. It’s not about what is advantageous, it’s about what survives the selection process. A combination of odds that play out. Our eyes are not advantageous or chosen by evolution, our eyes were just acceptable enough for us to survive while other variations were not. There was no decision or work/progress towards an end go…

No, I understand how natural selection works. I'm a fan of Stephen Jay Gould. Please keep in mind the original comment I was responding to: > Eggs are evolutionarily designed to survive falling out of nests and perches. My response is "no, they are not". First, like you said, they are not "designed" in any way. But that's the pedantic response. Second, there's no selective pressure for eggs resistant to dropping from…

That makes sense, thank you for clarifying.
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