Mar 18 14:26:31 ok then, let's begin Mar 18 14:27:35 okay :) Mar 18 14:28:02 So, last week, we've seen the logic paradoxes. Mar 18 14:28:21 And now, we'll focus on logic enigmas. Mar 18 14:29:10 But, as a transition, we may study "Hilbert's Hotel" Mar 18 14:29:52 This paradox was explained by Hilbert. Mar 18 14:30:00 He said : Mar 18 14:30:49 Let's take a hotel with an infinite number of rooms, and, let's assume all these rooms are occupied. Mar 18 14:31:21 Now, some tourists come to this hotel. Mar 18 14:32:11 If it was a finite-rooms-hotel, in the same situation, the tourists wouldn't be able to have a room in this hotel, but! here, since there's an infinity of rooms, what we can do is : Mar 18 14:32:33 move the guy from room 1 to room 2, the guy from room 2 to room 3, etc. Mar 18 14:33:14 Hence, all the new tourists can have a room in this infinite hotel. :) Mar 18 14:33:59 Now, let's imagine that an infinite number of tourists come to the hotel. Mar 18 14:34:18 We move 1 to 2, 2 to 4, 3 to 6, etc. Mar 18 14:34:35 So, the odd rooms are free for the newcomers. :) Mar 18 14:35:15 Did you get it all thus far? Mar 18 14:35:32 yepo Mar 18 14:35:49 :) Mar 18 14:35:58 k ;) Mar 18 14:36:04 uhm Mar 18 14:36:04 we had a hilarious diagram in our textbooks for this topic heh Mar 18 14:36:24 why can't you just put the newcomers in room 956743 Mar 18 14:36:25 ? Mar 18 14:36:39 you have to make it free Mar 18 14:37:02 hrm Mar 18 14:37:11 you could move the person from 956743 to 956744 and etc etc. if you want Mar 18 14:37:11 i thought you said they were all full? Mar 18 14:37:21 they are Mar 18 14:37:30 but, since there are an infinite amount of rooms Mar 18 14:37:35 there is no problem ;) Mar 18 14:37:53 of course, if the number of rooms was finite Mar 18 14:38:14 and, if they all were full, then, nobody could enter the hotel.. Mar 18 14:38:31 but, since we deal with infinity, we can put as many people as we want :) Mar 18 14:39:32 * _riftor (riftor@shytb0x-C0240CF7.plus.com) has joined #lecture Mar 18 14:39:32 * riftor has quit (Connection reset by peer) Mar 18 14:40:51 so, mu, is it better now? Mar 18 14:41:37 no Mar 18 14:42:02 tell me where is the problem ;) Mar 18 14:42:08 if there're are infinite rooms, they are infinitely full with an infinite number of guests Mar 18 14:42:16 so there is no place to move them Mar 18 14:42:25 thats why he starts from 1 Mar 18 14:42:28 :) you've reached the paradox Mar 18 14:42:31 moves them back Mar 18 14:42:41 mm Mar 18 14:43:00 you can always add elements to an infinite set Mar 18 14:43:10 and it'll still be infinite Mar 18 14:43:15 but you said they are all full! Mar 18 14:43:25 yes, we assume they are Mar 18 14:43:43 maybe i better stfu now and let you continue Mar 18 14:43:47 but, the point is that, when dealing with infinity, we can always create free space ;) Mar 18 14:44:02 =/ Mar 18 14:44:05 well, for a further reading on the topic, I suggest : http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel Mar 18 14:44:10 ty Mar 18 14:44:13 i'm done Mar 18 14:45:33 Ok, so actually, we are not going to deal with the concept of infinity tonight, so, I'll move to logic enigmas now. Mar 18 14:46:14 Let's begin with a classic, namely, the "hats' color" problem. :) Mar 18 14:47:01 lol Mar 18 14:47:09 sorry Mar 18 14:47:10 :( Mar 18 14:47:16 So, say there are three people sitting like : A -> B -> C ->, where the "->" represents the direction where the people look at. Mar 18 14:48:00 Now, we take four hats : two blue hats, and two red hats. Mar 18 14:48:21 We put three of them randomly on each of the guys' head. Mar 18 14:48:37 Now, we ask them to guess the color of their hats. Mar 18 14:49:01 And, the question is : Who'll be the first to guess, and why? Mar 18 14:49:41 any ideas? Mar 18 14:49:42 d Mar 18 14:50:01 cause he say the first threes hats Mar 18 14:50:04 saw* Mar 18 14:50:41 there's no "d".. Mar 18 14:51:04 lol my bad Mar 18 14:51:04 c Mar 18 14:51:55 why? Mar 18 14:52:12 cuz he saw the first twos hats Mar 18 14:52:23 actually, C can't see anything... Mar 18 14:52:27 no? Mar 18 14:52:28 m Mar 18 14:52:33 you have : A -> B -> C -> Mar 18 14:52:38 A sees B and C Mar 18 14:52:40 B sees C Mar 18 14:52:46 oh then its a Mar 18 14:52:50 C sees.. nothing Mar 18 14:52:59 well, this is only a partial answer Mar 18 14:53:13 in which case can A guess the color of his hat? Mar 18 14:53:17 A, becasue it sees b and c Mar 18 14:53:25 yes, but still Mar 18 14:53:32 remember that we took four hats Mar 18 14:53:40 two blue, and two red Mar 18 14:53:56 and, then, we picked randomly three of them Mar 18 14:54:10 that we put on the guys' head Mar 18 14:54:29 so, I agree with the fact that A can guess it first, but, not always Mar 18 14:54:43 that's why I repeat : in which case can A guess the color of his hat? Mar 18 14:56:53 beats me >;| Mar 18 14:57:11 ok, so, do you want me to explain? Mar 18 14:57:16 yes please Mar 18 14:57:29 alright then Mar 18 14:57:42 in fact, the best way is to draw the situation Mar 18 14:57:49 and to represent the possibilities Mar 18 14:57:54 i.e. : Mar 18 14:57:59 is their an online whiteboard anywhere? Mar 18 14:58:08 A = blue, B = red, C = red Mar 18 14:58:09 or Mar 18 14:58:21 A = blue, B = blue, C = red Mar 18 14:58:27 or Mar 18 14:58:44 A = blue, B = red, C = blue Mar 18 14:58:45 or Mar 18 14:58:56 A = red, B = blue, C = blue Mar 18 14:59:03 or Mar 18 14:59:13 A = red, B = red, C = blue Mar 18 14:59:18 or Mar 18 14:59:35 9 possiblilities.. Mar 18 15:00:36 no Mar 18 15:01:10 only 3! = 6 Mar 18 15:01:15 i.e. : Mar 18 15:01:33 RRB Mar 18 15:01:36 RBR Mar 18 15:01:42 BRR Mar 18 15:01:44 BBR Mar 18 15:01:47 BRB Mar 18 15:01:55 RBB Mar 18 15:01:59 ok? Mar 18 15:02:25 k Mar 18 15:02:50 ok, so now, let's see in which cases A can guess his hat color Mar 18 15:03:00 keep in mind he can see A and B Mar 18 15:03:34 and, he knows that, two of them (them = the three guys) have the same hat color Mar 18 15:03:46 so, if he sees : Mar 18 15:03:52 BB, he knows his hat is R Mar 18 15:04:06 if he sees RR, he knows his hat is B Mar 18 15:04:12 else, he cannot guess! Mar 18 15:04:16 do you see why? Mar 18 15:06:04 <_riftor> check Mar 18 15:08:51 * _riftor is now known as riftor-afk Mar 18 15:10:00 sorry guys go to afk for a while, cleaning my house Mar 18 15:11:05 ok, so, since you got the case where A can guess Mar 18 15:11:22 now, can you say who'll be able to guess the color in the other cases? Mar 18 15:13:38 Well, clearly, it is the 2nd guy. Mar 18 15:14:02 Indeed, if A doesn't speak, it means that him and the 3rd guy have different hat colors. Mar 18 15:14:18 So, he just has to look at the hat's color of the 3rd guy. Mar 18 15:14:30 If it's blue, then his hat is red. Mar 18 15:14:40 If it's red, then his hat is blue. :) Mar 18 15:16:11 * Elda_Winslacks (loulou@shytb0x-FD3BADAA.w83-192.abo.wanadoo.fr) has joined #lecture Mar 18 15:16:16 * riftor-afk has quit (Ping timeout) Mar 18 15:16:18 If this enigma has interested you, I advice you to take a look at : http://www2.binaryuniverse.net:81/forums/viewtopic.php?t=424 Mar 18 15:17:06 Now, let's see another case, namely, the "prisoners' dilemma". Mar 18 15:17:38 This one has been discovered by Melvin Dresher and Merill Flood in 1950. Mar 18 15:17:51 And, here it goes : Mar 18 15:18:06 two guys are arrested. Mar 18 15:19:02 they're put into two different prison cells. Mar 18 15:19:14 And, the inspector tells us : Mar 18 15:19:45 if they don't speak : 2 years for each Mar 18 15:19:58 if they say they're innocent : 4 years for each Mar 18 15:20:40 if one says he's innocent and the other doesn't speak : the 1st one is free and the other one goes in prison for 5 years. Mar 18 15:21:15 Now, what can they do? Mar 18 15:22:33 Well, basically, there are two possibilities : Mar 18 15:22:39 *1st one : Mar 18 15:23:14 Thinking they'll get free, most of the prisoners will denounce the other guy. Mar 18 15:23:32 But, since the other one will do the same, they'll both get 4 years. Mar 18 15:23:50 Indeed : Mar 18 15:23:52 the inspector forgot a possibily, if they say they are guilty Mar 18 15:24:58 no? Mar 18 15:25:14 same thing as the innocent case Mar 18 15:25:23 but, anyway, they wouldn't say they're guilty Mar 18 15:25:29 since, one of them is not Mar 18 15:25:49 ok Mar 18 15:25:53 Now, let's explain this 1st possibility : Mar 18 15:26:06 Say A is guilty. Mar 18 15:26:14 A deserves 5 years. Mar 18 15:26:35 If he denounces B, he knows he'll get at most 4 years. Mar 18 15:27:04 He doesn't really think he'll be free, B will say he's innocent. Mar 18 15:27:47 B can't stfu and take the risk to go in prison for 5 years while he's innocent, so, he'll certainly denounce A, and take 4 years. Mar 18 15:28:16 So, we can make an array : Mar 18 15:28:45 Deserve - Probably - Might be Mar 18 15:28:52 A : 5 - 4 - 0 Mar 18 15:29:01 B : 0 - 4 - 5 Mar 18 15:29:02 got it? Mar 18 15:32:04 ok Mar 18 15:32:19 alright, so let's see the other possibility: Mar 18 15:32:25 *2nd one : Mar 18 15:32:52 * Pixi3_1103 has quit (Quit: ) Mar 18 15:33:11 If they think together, they could have a better thing. Mar 18 15:33:20 Indeed : Mar 18 15:33:34 if A, the guilty man, doesn't speak, the array will look like : Mar 18 15:33:47 A : 5 - 2 - 5 Mar 18 15:33:59 B : 0 - 2 - 0 Mar 18 15:34:09 but, will A take this risk? Mar 18 15:34:21 Indeed, if B says he's innocent, A will get 5 years... Mar 18 15:34:26 no Mar 18 15:34:41 Therefore, it leads us to the following conclusion : Mar 18 15:35:08 We let the prisoners talk to each other, and we see that it doesn't change anything. Mar 18 15:35:22 They'll mainly choose the 1st possibility! Mar 18 15:35:39 Interesting dilemma, eh? Mar 18 15:35:55 chyeah Mar 18 15:36:26 well, if you want to read more stuff about that, you should see : http://pespmc1.vub.ac.be/PRISDIL.html Mar 18 15:36:35 rgr Mar 18 15:37:14 And, now, this will be our last topic, we shall discuss about one of the greatest geniuses ever.. Mar 18 15:37:27 einstien! Mar 18 15:37:32 w00t :) Mar 18 15:38:00 good Mar 18 15:38:37 Indeed, we'll now see, the so-known, Einstein's enigma. :) Mar 18 15:38:53 hes a jew too Mar 18 15:39:45 We'll see that : Mar 18 15:39:55 *the problem seems to be extremely hard Mar 18 15:40:04 *a powerful reasoning kills it Mar 18 15:40:30 *the use of a special tool makes this problem way easier Mar 18 15:40:43 which tool? Mar 18 15:40:49 *but, in both cases, what's needed is method and.. patience! Mar 18 15:41:02 Now, here goes the problem : Mar 18 15:41:13 Five men live in five houses of five different color. Mar 18 15:41:13 They smoke five different brands of cigar,drink five different beverages,and keep five different pets. Mar 18 15:41:32 Hypotheses : Mar 18 15:41:34 oh I know it! Mar 18 15:41:55 * The Norwegian lives in the first house. Mar 18 15:41:55 * The brit lives in the red house. Mar 18 15:41:55 * The Swede keeps dogs as pets. Mar 18 15:42:15 * The Dane (hey Ice, you here? :p) drinks tea. Mar 18 15:42:25 * The green house is just on the left of the white house. Mar 18 15:42:25 * The green house owner drinks coffee. Mar 18 15:42:25 * The man who smokes Blend lives next to the one who keeps cats. Mar 18 15:42:25 * The person who smokes Pall Mall rears birds. Mar 18 15:42:33 * The owner of the yellow house smokes Dunhill. Mar 18 15:42:34 * The man living in the house right in the center drinks milk. Mar 18 15:42:34 * The German smokes Prince. Mar 18 15:42:34 * The man who smokes Blend has a neighbor who drinks water. Mar 18 15:42:46 * The Norwegian lives next to the blue house. Mar 18 15:42:47 * The man who keeps horses lives next to the man who smokes Dunhill. Mar 18 15:42:47 * The owner who smokes Blue Master drinks beer. Mar 18 15:43:39 And, the question is : who keeps fishes? Mar 18 15:44:29 According to Einstein, 98% of the people in the world can't solve this enigma. :) Mar 18 15:44:36 :) Mar 18 15:44:41 Will you be part of these 98%? :P Mar 18 15:45:16 I think you should let us a little time to search the answer Mar 18 15:45:41 I never search because someone always put the solution but I don't remember Mar 18 15:46:11 Ok, so, I'll let you search ;) Mar 18 15:46:35 * mu-tiger thinks this could be solved with an algebraic equation Mar 18 15:46:45 :D Mar 18 15:46:58 mu-tiger gives me an occasion to go on Mar 18 15:47:15 but, i don't know how to set it up Mar 18 15:47:23 and explain what the usual solving methods are. Mar 18 15:47:40 To do things, there usually are two ways : Mar 18 15:48:01 -to do the stuff by oneself, whenever it's possible Mar 18 15:48:27 -or, to use tools to multiply by 10 our abilities Mar 18 15:48:46 For the intellectual problems, that's the same thing : Mar 18 15:49:07 -pure reasoning (by head) Mar 18 15:49:16 -else, using tools Mar 18 15:49:50 This is true for several subjects, such as : Mar 18 15:49:57 -algebra Mar 18 15:50:15 -and, obviously, else I wouldn't be saying all this stuff.. in logic! :) Mar 18 15:51:47 So, once again, let's build an array : Mar 18 15:52:06 To solve a problem : - Reasoning - Tools Mar 18 15:52:19 * b0re (b0re@shytb0x.com) has joined #lecture Mar 18 15:54:42 In math : it is possible to reason and find a solution - *when the problem is complex, it is useful to go and check algebra *we set equations with unknowns *solving these equations becomes algorithmic *in fact, the use of this way kind of.. doesn't need the hypotheses *and allows us to go into an almost mechanical solution Mar 18 15:55:25 sorry to interrupt Mar 18 15:55:28 but is someone logging tihs? Mar 18 15:55:38 In logic : it is possible to reason to find the solution - *when the problem is complex, it is useful to have tools Mar 18 15:56:16 *several diagrams have been invented, each of them being more or less efficient.. Mar 18 15:56:37 *anyway, they're adapted to some particular problems Mar 18 15:56:59 * riftor-afk (riftor@shytb0x-C0240CF7.plus.com) has joined #lecture Mar 18 15:57:01 *in our case, the recommended tool will be the : integram or logigram Mar 18 15:58:10 e.g. : http://members.lycos.nl/puzzel/puzzvben.html Mar 18 15:59:13 Now, did anyone of you get something? :) Mar 18 16:01:11 i'm still trying to think of an equation =/ Mar 18 16:02:29 I've found the color of each house Mar 18 16:02:44 keep working, then Mar 18 16:02:50 i'm a bit distracted Mar 18 16:09:52 So, did you find who keeps fishes? :) Mar 18 16:11:19 kick me when the lectures over, i gotta roll Mar 18 16:12:00 okay Mar 18 16:12:48 go on, then, pls, qwerty Mar 18 16:16:17 to solve this problem, I begin to do five case in which I put the thing that we know at the begining Mar 18 16:17:03 * ardnew (andrew@shytb0x-17FA9673.ok.ok.cox.net) has joined #lecture Mar 18 16:17:19 * Triple_Helix (omg@shytb0x-DEE576BC.vic.bigpond.net.au) has joined #lecture Mar 18 16:17:40 welcome, gentlemen of bso Mar 18 16:17:47 <.< Mar 18 16:17:48 thank you Mar 18 16:17:52 yw Mar 18 16:17:52 >.> Mar 18 16:17:53 behave Mar 18 16:17:59 i will Mar 18 16:18:01 ty Mar 18 16:18:05 try... Mar 18 16:18:08 no no Mar 18 16:18:10 you WILL Mar 18 16:18:11 xD Mar 18 16:18:21 i will try very hard to behave Mar 18 16:18:28 :/ Mar 18 16:18:33 ok Mar 18 16:18:35 * ardnew slaps Triple_Helix Mar 18 16:18:38 and thanks to this information, we know that some things can't be here or here, to I write it in the case and bar it, so I could deduce others information, and contnie like that Mar 18 16:18:39 Shape up Mar 18 16:18:49 * qwertydawom gives voice to Elda_Winslacks Mar 18 16:19:00 * qwertydawom sets mode +m #lecture Mar 18 16:19:03 * qwertydawom gives voice to mu-tiger Mar 18 16:19:09 ty Mar 18 16:19:23 go on, pls, Elda_Winslacks Mar 18 16:23:35 so i found the solution Mar 18 16:23:48 It's the german Mar 18 16:24:04 yes, that's right :) Mar 18 16:24:48 for example to begin you know that in the house in the middle, the man drinks milk Mar 18 16:25:03 so you can write milk in the other case and bar it Mar 18 16:25:22 pls excuse me a moment, Elda_Winslacks Mar 18 16:25:32 how did you find your solution? Mar 18 16:25:36 and it is as I say before, if you do that for each affirmation, you can find other information Mar 18 16:26:28 and when you are near the end if you have bar four things for the same caracteristic you know it's the last Mar 18 16:26:37 very nice! Mar 18 16:26:41 thank you Mar 18 16:26:43 go on, pls Mar 18 16:26:59 (in fact it take a little time, but we can find it like that) Mar 18 16:27:32 yes Mar 18 16:27:43 so I can try to remenber the begining Mar 18 16:28:00 fisrt you put the norvegian in the first house Mar 18 16:28:41 after the milk in the middle Mar 18 16:28:45 yes Mar 18 16:28:56 so you bar it in the other houses Mar 18 16:29:42 you can also bar tee in the first house because it's the N who is in the house and it's the D who drinks tee Mar 18 16:29:54 yes Mar 18 16:30:09 then the blue house is the second Mar 18 16:30:23 ok? Mar 18 16:30:30 and that is about where i started searching for an algebraic equation Mar 18 16:30:36 ;) Mar 18 16:30:43 my respect to you, elda Mar 18 16:30:58 thnaks... Mar 18 16:31:12 you're very welcome and deserving Mar 18 16:31:16 and did you find the solution with your method? Mar 18 16:31:19 pls continue Mar 18 16:31:21 no Mar 18 16:31:26 i am distracted Mar 18 16:31:39 ok if you like, but it's a bit long Mar 18 16:31:48 is it alright, qwertydawom? Mar 18 16:32:26 i ask you a little time because I didn't write the etap, so I have to do again what I did Mar 18 16:32:53 oh no! Mar 18 16:33:01 pls don't feel obligated Mar 18 16:33:19 no problem Mar 18 16:33:20

is it alright, qwertydawom? --> yes, it is :) Mar 18 16:33:26 :) Mar 18 16:33:27 ty Mar 18 16:34:02 yw Mar 18 16:34:11 you you also know that the green house is not the third Mar 18 16:34:34 because he drinks tee instead of milk Mar 18 16:34:52 yes Mar 18 16:36:12 so because the green house is nexto to the white, you know that the white is the last and the green the house just before Mar 18 16:36:55 * IceDane (IceDane@F39DB507.E312044D.8340D7F9.IP) has joined #lecture Mar 18 16:37:04 then you know that the english lives in the red house, so the red house is not the first Mar 18 16:37:15 so it's the fourth Mar 18 16:37:48 we know the color of four house so we deduce that the first is yellow Mar 18 16:38:16 the english is in the third Mar 18 16:38:23 * ardnew (andrew@shytb0x-17FA9673.ok.ok.cox.net) has left #lecture Mar 18 16:38:30 * b0re has quit (Quit: http://shytb0x.com ..its a website) Mar 18 16:39:13 and now we know that the first house is yellow so he smokes Dunhill Mar 18 16:39:32 do you want I go on? Mar 18 16:40:05 yes, pls Mar 18 16:40:38 so because the horse is next the man who smokes Dunhill, horse is in the second house Mar 18 16:41:34 ( don't forget that everutime we find something, we bar it in the other cases) Mar 18 16:42:02 * qwertydawom gives channel operator status to mu-tiger Mar 18 16:42:33 I didn't remenber if I said that the man in the fourth house drinks cafe Mar 18 16:42:39 no, not yet Mar 18 16:43:56 * qwertydawom has quit (Quit: see y'all!) Mar 18 16:44:11 we know that in the fourth house the man doesn't smoke Whinfield (because he drinks cafe instead of beer) Mar 18 16:45:07 quertydawom has to go Mar 18 16:45:16 yes Mar 18 16:45:18 but I finish the explanation Mar 18 16:45:24 thank you :) Mar 18 16:46:10 we know that the N drinks water Mar 18 16:47:00 yes Mar 18 16:47:03 because he doesn't drink tee, nor cafe, nor milk, nor beer (because it's the smoker of whinfield) Mar 18 16:47:08 right Mar 18 16:47:24 and so the second smokes malboro Mar 18 16:47:40 so we can bar it in the other cases Mar 18 16:47:51 ok Mar 18 16:48:23 in the fourth house **** ENDING LOGGING AT Sat Mar 18 16:49:25 2006