

Title: Unsolved Problems in the Hard Forum Post by Icarus on Jul 23^{rd}, 2003, 9:01pm New Stuff
Puzzles with no solution to the original problem (but likely to be solvable).
Puzzles with possible solutions, solutions not clearly demonstrated, or solutions which have been seriously contested.
Puzzles with incomplete solutions (but likely completable.)
Puzzles with incomplete solutions (and unlikely to ever be completed.)
Solved puzzles with open side challenges.
Latest Changes (11/11/03):
Link to Change History (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1059019294#12). (Or you could just scroll down to the 12th post! ;)) 

Title: Re: Unsolved Problems in the Hard Forum Post by aero_guy on Jul 23^{rd}, 2003, 10:29pm Damn, thanks. This will help direct efforts. Must have taken a while too. 

Title: Re: Unsolved Problems in the Hard Forum Post by SWF on Jul 24^{th}, 2003, 11:07pm Great work, Icarus! This list will be very helpful to keep track of the riddles that slip through the cracks. The Intersecting Spheres (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1049998432) problem looks like it was first solved by cho. There was much sidetrack discussion and debate in the thread, but the question asked was simple and cho answered it. Many of the hard problems are not likely to ever be solved fully in this forum, and separating these from the more tractable problems would be useful. It would also be nice to include some sort of status, such as "best 100 prisoners and lightbulb solution so far takes 3536 days", but I guess it is tough to verify the accuracy of such claims. Unfortunately, the prisoners and lightbulb thread was taken over by repeated irrelvant suggestions from posters who did not read the thread and any serious solution posted there is likely to get buried in posts suggesting to break the bulb into 100 pieces. 

Title: Re: Unsolved Problems in the Hard Forum Post by Lightboxes on Aug 13^{th}, 2003, 9:10pm ... Quote:
Hey!, I was new here, I didn't know how to approach these problems. :) And I do regret it okay! sheesh. Hehe 

Title: Re: Unsolved Problems in the Hard Forum Post by william wu on Sep 9^{th}, 2003, 9:03am Ditto. Awesome work Icarus, as always. Thanks so much :) 

Title: Re: Unsolved Problems in the Hard Forum Post by James Fingas on Sep 23^{rd}, 2003, 1:28pm For Fitting Circles in Rectangles (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1057118716): my solution is, of course, correct, and my diameter is almost perfectly optimal, but I would like to point out that I proposed a side question that hasn't been answered (reply #7 in that thread). What if M and N weren't restricted to integers? 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Sep 23^{rd}, 2003, 6:00pm Okay! Okay! Okay! I know I've been letting this slide! I actually started on an update last weekend, but got sidetracked while investigating a posted solution, and never got back to it. Unfortunately, I'm having connection problems, so I may not be able to get to it tonight either. 

Title: Re: Unsolved Problems in the Hard Forum Post by SWF on Sep 23^{rd}, 2003, 6:25pm Icarus, since you are updating, I think you should reconsider whether the following are unsolved: Tunnels of Callicrates (although when the question is not clear, it is hard to tell when it has been answered), Language Proficiency Verification, Random Line Segment in Square, and Infinite Checkerboard. Also, how about putting the date of last update in the subject title. Since your changes are edits, they do not register as a new post to the thread and may otherwise go unnoticed. There are unsolved problems in the Easy and Medium section too. Maybe they should be moved to Hard. 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Sep 23^{rd}, 2003, 6:55pm I was unsure about that. Every so often a thread will move to the front of the forum, but when I look in it, I don't see any new posts. I had assumed this was the result of someone modifying their post. Now I realize (because of an incident while fixing thread titles in the Easy forum) what must be happening: if you post to a thread and then immediately delete it, the thread still gets counted as "modified". So what I will do is: every time I modify the list, I will also add and delete a blank post. That should bring up the "new" flag for everyone. Of course  this requires that I buckle down and work through figuring out what all needs to be changed! :( That's what I get for doing something ambitious once. ;) 

Title: Re: Unsolved Problems in the Hard Forum Post by James Fingas on Sep 24^{th}, 2003, 9:44am Yeah ... while you're slaving away being ambitious and all, I'm working hard keeping everybody's expectations low. If nobody thinks you're going to do anything, you don't have to! 

Title: Updated 12balls (variation) Post by Rujith de Silva on Oct 14^{th}, 2003, 9:22am I provided the answer for redPepper's extension (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1050065099) to the 12ball (variation), so this can probably be removed from the Unsolved Riddles. Thanks for putting together this list, by the way!  Rujith. 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Oct 14^{th}, 2003, 7:58pm I'll get it in my next update  which may be a while yet. I've got to find some spare time when I am not also feeling the call of other things. These are few and far between. 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Nov 11^{th}, 2003, 6:59pm Change History 9/25/03: I moved Robin Friberg's crypto puzzles to the medium thread, so while BNC's reply crypto (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1064534829#4) remains unsolved, it is no longer "Hard".;) SWF has solved Jamie's Poor Willy (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1059648982). Removed Infinite Checkerboard (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1028324447), although there is a side problem with no POSTED solution, I'm trusting Eric's statement that it is almose trivial from James' last post. Several category changes. Updated "New Stuff". 9/14/03: Removed Littlewood's Number game (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1040095764), as SWF has posted a good solution. Also updated some thread names. 8/16/03: Removed Willy's true colors (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1032197104), as it is now solved. Added the "New Stuff" section, to keep track of new problems that look like they might be around for a while. 8/3/03: Removed Another Fork In The Road (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1055514975), as SWF has posted the solution. Also included the side question Barukh has posted in the Lion Tamer puzzle. 7/29/03: Removed Intersecting Spheres (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1049998432) after convincing myself that Cho is correct. Also added this history, to make it easier to see what changes have been made. 7/28/03: Removed the Crazy Christmas Game (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1042232196), since SWF has posted a solution. I also reorganized the problems into categories, as SWF suggested. Thanks to William for making the thread sticky. 7/24/03: After rereading the Sleeping Beauty (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1049844608) thread in response to Rmsgrey's new post, I see that it is among the solved puzzles for which I failed to notice the solution when scanning to create this list. I have removed it. 

Title: convex set projection Post by pjay on Dec 3^{rd}, 2003, 4:43am my kneejerk reaction to this problem is to triangulate the boundary of the convex set, but then i realized that the existence of a triangulation is not obvious and hard to prove, so i tried to think of another way. after looking at the hints it seems clear that willie is suggesting the triangulation approach. a comment before i proceed: i think maybe it should be stated that you can assume that the boundary of any convex set can be triangulated with arbitrarily small triangles? maybe this gives away too much?? dunno. anyways, here goes. take the dot product of 2 unit vectors to get cos(x) where x is the angle between them. letting one vector roam over a sphere and integrating we get: \int_0^\pi (2\pi cos(x)sin(x))/4\pi dx. use the identity 2 cos(x)sin(x)=sin(2x) to see that the above is equal to 1/4. now let the other vectot represent the height of a given triangle in the triangulation (as in a riemann sum approximation). by integrating over the triangle we get A/4 where A is the area of the triangle. now by taking the limit of triangulations we are done... 

Title: Re: Unsolved Problems in the Hard Forum Post by neopetsaddict on Jan 5^{th}, 2005, 9:40am ???ahhh could someone please help me ...for 2 weeks ive been trying to figure this riddle i cant .....(((riddle is what do u feed a sick bird....))) oh by the way im new this place looks kinda cool i love riddles but this one has stumped me big time ??? 

Title: Re: Unsolved Problems in the Hard Forum Post by william wu on Jan 5^{th}, 2005, 10:51am Neo, in the future please post such problems in a different section of the forum; this thread is for problems that have not been resolved after a long period of time. Answer: Tweetment! :) 

Title: Re: Unsolved Problems in the Hard Forum Post by THUDandBLUNDER on Jan 5^{th}, 2005, 11:38am on 01/05/05 at 09:40:31, neopetsaddict wrote:
Well, it helps if you get the wording right. 

Title: Re: Unsolved Problems in the Hard Forum Post by THUDandBLUNDER on Mar 21^{st}, 2005, 1:15am LEMMAS: Contrapositive (i) A => B = B' => A' de Morgan's laws (ii) (A or B)' = A' and B' (iii) (A and B)' = A' or B' (iv) (A => B) and (C => D) implies (A and C) => (B and D) (v) (A and B) => (C and B) implies (A => C) (vi) (A and B) => C and (D and E) => C' implies (A and B and D) => E' (vii) (A and B) => C and (C' and B) => A implies B'  Let D = Dance on tightropes E = Eat pennybuns Y = Young (equals 'not old') G = liable to Giddiness T = Treated with respect W = Wise B = go up in Balloons U = takes an Umbrella R = look Ridiculous L = may Lunch in public F = Fat Rewrite the statements as: 1) D' and E' => Y' 1a) (D or E)' => Y' (de Morgan) 1b) Y => D or E (contrapositive) 2) P and G => T 3) W and B => U 4) R and E => L' 4a) L => (R and E)' (contrapositive) 5) Y and B => G 6) F and R and D' => L 7) W and G => D' 8) P and U => R 9) D' and T => F Eliminating E from 1b) and 4a) using (iv) we get 10) Y and L and R => D Eliminating T from 2) and 9) using (iv) we get 11) P and G and D' => F Eliminating U from 3) and 8) using (iv) we get 12) W and P and B => R Combining 6) and 11) using (iv) we get 13) P and G and R and D' => L Combining 10) and 13) using (iv) and (vii) we get 14) Y and P and G => R' Combining 12) and 14) using (vi) we get 15) W and P and B and G => Y' So we now have 5) Y and B => G 7) W and G => D' 15) W and P and B and G => Y' From 5) Y => B' or G From 7) W => D' or G' From 15) W and P and Y => B' or G' Adding, W and Y and P => B' and (D' or G') (by (iv)) => B' and (D and G)' (by de Morgan) => [(B or (D and G)]' (by de Morgan) Hence B or (D and G) => (W and Y and P)' (by contrapositive) Therefore no wise young pigs are balloonists or (dance on tightropes and are liable to giddiness). 

Title: Re: Unsolved Problems in the Hard Forum Post by towr on Mar 21^{st}, 2005, 5:36am on 03/21/05 at 01:15:15, THUDandBLUNDER wrote:
Can you prove these lemmas? Because I don't think they're true.. (for (v) take A=true, B=C=false, for (vii) take A=B=C=true) 

Title: Re: Unsolved Problems in the Hard Forum Post by THUDandBLUNDER on Mar 21^{st}, 2005, 6:31am on 03/21/05 at 05:36:53, towr wrote:
A means A is true (given). A' means A is false. For (vii) A and B => C C' and B => A => A and B => C Contradiction; Therefore B' 

Title: Re: Unsolved Problems in the Hard Forum Post by towr on Mar 22^{nd}, 2005, 6:39am It's not clear how "C' and B => A => A and B => C" is to be read. Besides, a truth table shows that ([(A and B) => C] and [(C' and B) => A]) implies B' isn't a valid schema. 

Title: Re: Unsolved Problems in the Hard Forum Post by rmsgrey on Mar 22^{nd}, 2005, 6:58am Actually, looking at it, the contradiction appears to be valid, meaning that the premise must be false. The error appears to lie in only considering part of the premise  I get B' or C as the correct conclusion. 

Title: Re: Unsolved Problems in the Hard Forum Post by THUDandBLUNDER on Mar 23^{rd}, 2005, 1:12am Well spotted, towr and rmsgrey. Hence we have (A and B)' or (C' and B)' equals (A' or B') or (C or B') (de Morgan) equals A' or (B' or C) But as A' => (B and C')' (contrapositive) equals (B' or C) (de Morgan) we can conclude simply A', can we not? But wait, if (C' and B) is false then we cannot use the contapositive, right? Jeez, I used to think this stuff was easy! 

Title: Re: Unsolved Problems in the Hard Forum Post by rmsgrey on Mar 23^{rd}, 2005, 7:03am on 03/23/05 at 01:12:38, THUDandBLUNDER wrote:
You have: A' or D and A' => D where D is (B' or C) they can be rewritten as: (A and D')' (de Morgan) and (A' and D) or (A and D) or (A and D') which gives: (A' and D) or (A and D) which rearranges to: (A or A') and D which simplifies to: D (which is (B' or C)) 

Title: Re: Unsolved Problems in the Hard Forum Post by rmsgrey on Mar 23^{rd}, 2005, 7:28am on 03/23/05 at 01:12:38, THUDandBLUNDER wrote:
A => B is always precisely as true as B' => A' regardless of whether A, B or both are true or false, so the contrapositive is always valid. 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Mar 23^{rd}, 2005, 3:00pm Question: why has all of this been posted here instead in the appropriate thread? 

Title: Re: Unsolved Problems in the Hard Forum Post by THUDandBLUNDER on Mar 23^{rd}, 2005, 3:57pm on 03/23/05 at 15:00:15, Icarus wrote:
Answer: Because the appropriate thread appears to have been locked by someone with a poor memory. :P 

Title: Re: Unsolved Problems in the Hard Forum Post by Icarus on Mar 23^{rd}, 2005, 7:17pm I'm not sure why it was locked, unless it is because it was one of your infamous disappearing post threads. In particular, the original post is gone, which means there is no version of the original riddle available. I have unlocked the thread, but the discussion might as well continue here, since I have pretty much let this thread slide. 

Title: Re: Unsolved Problems in the Hard Forum Post by linnea on Aug 14^{th}, 2007, 10:14am Can someone please answer this riddle? [b][/b]What is brighter than light, but darker than night. Kings and Queens want it,yet peasants have it. If you eat it you will die. 

Title: Re: Unsolved Problems in the Hard Forum Post by towr on Aug 14^{th}, 2007, 11:02am on 08/14/07 at 10:14:25, linnea wrote:
Unless you've come up with anything. But then you wouldn't be asking. 

Title: Re: Unsolved Problems in the Hard Forum Post by JohanC on Aug 14^{th}, 2007, 11:35am on 08/14/07 at 11:02:11, towr wrote:
It is very healthy having it in your eyes. You're less fortunate having it in you stomach. 

Title: Re: Unsolved Problems in the Hard Forum Post by towr on Aug 14^{th}, 2007, 11:48am There is much ado about it, according to Shakespeare 

Title: Re: Unsolved Problems in the Hard Forum Post by linnea on Aug 15^{th}, 2007, 9:51am Thanx. You are really smart. Either that or I'm stupid. hahaha.... 

Title: Re: Unsolved Problems in the Hard Forum Post by rmsgrey on Aug 15^{th}, 2007, 10:55am on 08/15/07 at 09:51:04, linnea wrote:
Or we've just heard it before... 

Title: Re: Unsolved Problems in the Hard Forum Post by pscoe2 on Jan 9^{th}, 2010, 10:13am on 08/14/07 at 10:14:25, linnea wrote:
Can the answer be peace... I mean it is symbolised by white and is highest in the night ...kings and queen want peace but the peasent has it...the last part dosent fit :P 

Title: Re: Unsolved Problems in the Hard Forum Post by brac37 on Jan 28^{th}, 2010, 11:12am on 01/09/10 at 10:13:19, pscoe2 wrote:
No, that is not the correct answer. 

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