[HN Gopher] "I don't know the numbers": a math puzzle ___________________________________________________________________ "I don't know the numbers": a math puzzle Author : otras Score : 34 points Date : 2022-05-08 21:49 UTC (1 hours ago) (HTM) web link (alexanderell.is) (TXT) w3m dump (alexanderell.is) | kej wrote: | I like puzzles like this, where it's not just "what does each | person know?" but also "when did they know it?" | | Another similar puzzle, with more logic and fewer numbers, is | this one which was nicely written up on xkcd: | https://xkcd.com/blue_eyes.html | [deleted] | conradludgate wrote: | That was a good puzzle. I won't put the answer here for | spoilers, but there is a neat solution. | | If you get stuck, try imagine a different number of blue/brown | eyes on the island and what that might change | xdfgh1112 wrote: | Billed as "the hardest logic puzzle in the world". Now I feel | less dumb for not solving it myself when it appeared in | Cracking the Code Interview. | thaumasiotes wrote: | > this one which was nicely written up on xkcd | | But there's not a writeup there. That's just a statement of the | problem. | | This is not the hardest logic puzzle in the world, though | stating the answer can be tricky. If it takes one day for a | solitary blue-eyed person to realize he's the one with blue | eyes and leave, then it takes 100 days for a group of 100 blue- | eyed people to realize they have blue eyes and leave. | | The blue eyes puzzle relies on everyone receiving input from | the same synchronized digital clock ("Every night at midnight, | a ferry stops at the island"), which is unusual for a logic | puzzle. The puzzle here is similarly discretized, but it's more | a pure question of sequence - each line of dialog happens after | the previous line, and that's all that matters. | xdfgh1112 wrote: | https://xkcd.com/solution.html | lisper wrote: | Bonus meta-puzzle: the puzzle as stated is actually unsolvable. | Both Sandy and Peter have to know something that the puzzle | implies but does not actually stipulate that they know. What is | it? | onionisafruit wrote: | 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. | nicoburns wrote: | That the other person is following the same system as them to | decide whether they "know the numbers". It would be super easy | for one of them to say they don't know for some other reason, | in which the others' reasoning would be false. | ghayes wrote: | That the order of the numbers is unimportant? Otherwise every | non-duplicate solution has a correlate solution, inverted. E.g. | (3,2) implies (2,3) is also a solution. | onionisafruit wrote: | I don't think that's necessary. The problem only says there | are two numbers, not that the numbers have any order. | taormina wrote: | The number of steps it would take to solve the puzzle. | thaumasiotes wrote: | No, they discover that as they talk. It's not something they | need to know; it's something you need to know. | arjvik wrote: | That both are perfect logicians with an understanding of the | system sans the information about the two numbers themselves? | pvg wrote: | Yesterday: | | https://news.ycombinator.com/item?id=31269698 | kdheepak wrote: | 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 breaks when dropped from a floor, then it would also | have broken from any floor above that. If an egg survives a fall, | then it will survive any fall shorter than that. | | > The question is: What strategy should you adopt to minimize the | number egg drops it takes to find the solution? (And what is the | worst case for the number of drops it will take?) | | I wrote up a solution for this (along with a generalized | analytical solution) on my blog: https://blog.kdheepak.com/the- | egg-tower-puzzle | moron4hire wrote: | The solution is 0 floors. Eggs can't survive very far falls. | | EDIT: I know "that's not the point, the point is the math." But | mathematicians need to understand that math isn't the point, | understanding the world is. And in our world, the one we | actually inhabit, eggs don't survive more than a few inches of | drop. So it's an eggcellent example of how terrible | mathematicians are as teachers and communicators. | danachow wrote: | Lol. Someone needs some fresh air. | [deleted] ___________________________________________________________________ (page generated 2022-05-08 23:00 UTC)