“I don't know the numbers”: a math puzzle • Hacker News Board

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

#61

Post by hamburglar » Mon, May 09, 2022, 3:13 AM UTC

Layke1123 wrote: post #59

moron4hire wrote: post #9

Earlier quoted context omitted.

Quoted post unavailable.

I hate how you are downvoted for an accurate statement. I love math, but I've come to understand from a teacher's perspective how accurate your statement can be. I liked your insight.

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.

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

#62

Post by PebblesRox » Mon, May 09, 2022, 3:13 AM UTC

moron4hire wrote: post #9

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

Quoted post unavailable.

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 engage with the math as it's intended to be engaged with.

In a classroom setting, on the other hand, I think it's best to stay away from pseudocontext. Either make the context realistic, make it clearly fantastical, or just use math as the context without trying to dress it up in real-life details.

Pseudocontext in a teaching environment is problematic because it requires learners to ignore the common-sense reasoning that they'd apply to a real-life problem and it reinforces the impression that math has nothing to do with the real world.

In this case, we could call it a dragon egg and that would be enough I think to transform it into a fantasy context, since nobody has preexisting assumptions about how durable a dragon's egg might be.

[0] https://blog.mrmeyer.com/2010/pseudocontext-saturdays-introd...

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

#63

Post by kthejoker2 » Mon, May 09, 2022, 3:35 AM UTC

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 have to see to my eldest child who is in bed with measles." The census taker departs, satisfied.

https://en.wikipedia.org/wiki/Ages_of_Three_Children_puzzle?...

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

#64

Post by otras » Mon, May 09, 2022, 3:41 AM UTC

isaacg wrote: post #54

After the elimination of candidates due to Peter's first comment, the entry in the product map with value 7920 should also have the candidate (80,99). The whole point of this step is that there should be no single-candidate entries left in product.

Oh yes of course, I must have missed copying that over. Thanks!

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

#65

Post by Layke1123 » Mon, May 09, 2022, 3:47 AM UTC

hamburglar wrote: post #61

Layke1123 wrote: post #59

Earlier quoted context omitted.

I hate how you are downvoted for an accurate statement. I love math, but I've come to understand from a teacher's perspective how accurate your statement can be. I liked your insight.

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 "correct" speech on Hacker News.

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

#66

Post by photochemsyn » Mon, May 09, 2022, 4:02 AM UTC

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

Wouldn't one normally just try to convert this to an unambiguous discrete problem, something like:

Given:

(1) the ordered sequence of whole numbers (1, 2, ... , 99, 100) and

(2) an unknown value N that is a member of this sequence,

(3) the following tests (a candidate is a guess at the value of N), and two separate threads to run tests:

(A) if candidate (B) candidate > N : false & thread terminates (no more candidates can be checked with that thread)

Determine the best strategy for finding N (minimize the number of tests while leaving at least one thread alive)

Determine the worst case for the number of tests needed to find N using this optimal strategy.

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

#67

Post by ctxc » Mon, May 09, 2022, 4:21 AM UTC

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

I'm not too math-y, but this did capture my sense of wonder.

However, it was short lived since now I know it takes "14 drops" maximum, but not the solution - "which floors should I use the 14 drops on though?"

Maybe I'd be intrigued enough to try and follow the math if that was added in :)

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

#68

Post by edflsafoiewq » Mon, May 09, 2022, 4:43 AM UTC

613style wrote: post #57

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

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.

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

#69

Post by jimmygrapes » Mon, May 09, 2022, 5:30 AM UTC

moron4hire wrote: post #9

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

Quoted post unavailable.

This was also my first thought, as an admitted deficient with any math beyond (and sometimes including) arithmetic. My second thought was: did you not consider that eggs differ from one another?

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

#70

Post by vivegi » Mon, May 09, 2022, 6:08 AM UTC

kdheepak wrote: post #8

That was a fun puzzle. I have another one that is math puzzle: > You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. > If an egg b…

> The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. (emphasis added)

The egg doesn't break when dropped out of the window (i.e., instantaneously). It potentially breaks when it hits the floor after a time delay t. So, the answer is 100 and 0 trials.

ps: This is a joke. Don't take it too seriously.