[HN Gopher] "I don't know the numbers": a math puzzle
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"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]
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