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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

#41

Post by niccl »

the_af wrote: post #29
jammaloo wrote: post #25

Earlier quoted context omitted.

On August 22, 1994, David Donoghue threw an egg out of a helicopter onto a golf course in the UK, from a height of 213 meters (700 feet). He now has the record for the longest egg drop without breaking in the world (all without an outside structure for added protection!). https://www.scienceworld.ca/resource/egg-drop/ Eggs are evolutionarily designed to survive falling out of nests and perches. You assume that the eg…

> Eggs are evolutionarily designed to survive falling out of nests and perches. I wonder about this. Realistically, what fate awaits the egg that dropped from the nest in the tree branch, even if it survives the fall?

plus, there's a cost to the parent in making the egg shell arbitrarily drop-proof, so there's a balance of resources required to survive drop versus genetic benefit of surviving the drop

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

#43

Post by oh_sigh »

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 building is on the moon. Happy now? No of course you aren't.

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

#44

Post by otras »

Arnavion wrote: post #40

In case anyone else is confused like I was, the article is wrong about Sandy's first round. The article claims she can eliminate (1, 4) on the basis that it's the only pair that adds up to 5, but the author forgot about (2, 3), which was not eliminated by Peter's first round because it has the same product as (1, 6). The algorithm itself is correct, and the answer it arrives at is correct.

Oh good catch, I even crossed out the right ones in the above code block. Edited to be (2, 2), which is a better example (since (1, 3) was already cleared out). Thanks!

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

#46

Post by x-complexity »

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 point of the thought experiment is to get the non-math-inclined thinking about how they would try to get to the desired result within a limited set of tries: Practical considerations are to be ignored specifically for this purpose.

By going against the intentions of the thought experiment and blurting out "0 floors, eggs can't survive very far falls", the individual is deliberately trying to stamp out creativity & problem solving skills, as well as any attempts at getting others thinking about their approaches to the aforementioned problem. To them, the strict adherence to practical reality must be imposed 100% of the time, and there should be no time for playful thinking.

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

#47

Post by seoaeu »

Did I miss it, or does the article not actually explain why we know that at least one pair can be eliminated every round? It seems plausible that the process could get "stuck" in a place where Peter and Sandy both don't learn anything new from discovering the other doesn't know the answer yet.

(The puzzle being solvable means that they can't actually get stuck, but that feels like outside information...)

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

#48

Post by danachow »

GuB-42 wrote: post #39
moron4hire wrote: post #9

Earlier quoted context omitted.

Quoted post unavailable.

Eggs can absolutely survive very far falls. You are making a lot of assumptions here. Like: - This is a typical bird's egg. Most insect eggs for instance can survive any fall. - This is a hard floor, not water, snow,... - There is nothing to protect the egg. - Floors are typical ~3m floors, not floors from a doll house. - The experiment is done on earth The point of maths is that it doesn't need to be grounded into t…

> I am not sure a 100 story building exists (there is 101, but exactly 100?)

IIRC, the Hancock tower, briefly the 2nd tallest building in the world and then Chicago is 100 floors.

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

#49

Post by Forgeties79 »

niccl wrote: post #41
the_af wrote: post #29

Earlier quoted context omitted.

> Eggs are evolutionarily designed to survive falling out of nests and perches. I wonder about this. Realistically, what fate awaits the egg that dropped from the nest in the tree branch, even if it survives the fall?

plus, there's a cost to the parent in making the egg shell arbitrarily drop-proof, so there's a balance of resources required to survive drop versus genetic benefit of surviving the drop

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

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

#50

Post by otras »

seoaeu wrote: post #47

Did I miss it, or does the article not actually explain why we know that at least one pair can be eliminated every round? It seems plausible that the process could get "stuck" in a place where Peter and Sandy both don't learn anything new from discovering the other doesn't know the answer yet. (The puzzle being solvable means that they can't actually get stuck, but that feels like outside information...)

You’re totally right: there’s no guarantee that the candidate list continues to shrink, and there’s no guarantee that it won’t get stuck. For this problem, we are able to leverage the fact that it ends after 15 rounds, so the problem is less “run it until it finds a solution” and more “find the solution after exactly 15 rounds”.

In fact, if you let it run past 15 rounds (for N=100, at least), and check the number of disqualified candidates between rounds, you’ll find that it does get stuck in after 15 rounds as the candidate list doesn’t change. The flip side of this is that there are also solutions before 15 rounds, too, but with the problem’s original statement, we’re looking at exactly 15.

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