Guest Fadi Posted April 8, 2002 Report Share Posted April 8, 2002 I think I have the answer... I Think this is supposed to explain it. "No one will be at a disadvantage." If the white hat was on the head of one of those persons, the one that has the white hat on his head will be disadventaged, because the other two would know they got a black one by seeing it... Harut told that no one will be disadventaged, then everyone of those three are supposed to have the same color of hat in order that everyone have the same chance... (If that is not the answer you have, I think it would also be a good answer. No ?) But since that job would have been a computer one, since you and him want it, then, Seaphan gotting it before me would have been only because I will have left one of you two got the job. [ April 07, 2002, 12:24 PM: Message edited by: Domino ] Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 8, 2002 Report Share Posted April 8, 2002 Actualy I think its the only possible answer, if it is a logical answer you are waiting... Or better to say, it is the only logical answer I see. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 9, 2002 Report Share Posted April 9, 2002 Sip That wasnt funny, bad boy Don't be so fast, you may lose your hairs also I just wonder why people stop to answer me everytime I bring this x-x thing... you agree with me Sip right ? Quote Link to comment Share on other sites More sharing options...
Azat Posted April 9, 2002 Report Share Posted April 9, 2002 Oh great. Not only family members make fun of me loosing my hair, not HyeForum members do too. Oh wait, not much left to tear away. Domino, I agree with you about (x-x), I am just pulling your leg. Quote Link to comment Share on other sites More sharing options...
Sip Posted April 9, 2002 Report Share Posted April 9, 2002 quote:Originally posted by Edita:Hi:)2+2=5,How it happens????????????Ok I'll do the Engineering proof: 2.4 + 2.4 = 4.8 (2 significant digits)2 + 2 = 5 (1 significant digit) Welcome to the world of digital computers!!! Quote Link to comment Share on other sites More sharing options...
Sip Posted April 9, 2002 Report Share Posted April 9, 2002 OK here's one of my favorites ... I remember it from my undergrad discrete math class (that was one of the most fun math classes I have ever taken). Problem:There are 50,000 people in a small town. Can you find 2 people in that town that were born on the same day? Can you prove it? Quote Link to comment Share on other sites More sharing options...
Harut Posted April 9, 2002 Author Report Share Posted April 9, 2002 Sip, only two people on the same day, or at least two people on the same day? well, my caluclator gives this answer. in order everyone to be born on separate days, at least one of them must be at least136.986301369863013698630136986301 years old. when you find him we will continute to talk. =============== that remidered me of one similar problem. PROBLEMare there people in the world that have the same number of hair? and why? [ April 09, 2002, 12:20 AM: Message edited by: Harut ] Quote Link to comment Share on other sites More sharing options...
Sip Posted April 9, 2002 Report Share Posted April 9, 2002 Cool Harut jan ... if people are less than 130 years (not a bad assumption), then there must be at least 2 people with the same b-day. About the hair thing, I am going to say YES. In about 20 years, I will probably have the same amount of hair as Azat ---> Quote Link to comment Share on other sites More sharing options...
Sip Posted April 9, 2002 Report Share Posted April 9, 2002 I pretty much forgot what the x-x thing was really about ... I think it was that polynomial thing right? x-x is usually 0 in my world. But I agreed with you about when things go to infinity and you have 0/0 or inf/inf or things like that. However, if I have: a=ba-b sometimes is not 0 in what I do!!! but a-a and b-b are almost always 0. But that's just an artifact of finite precision arithmatic of computers. Actually, I think that (x-x) can be used to prove Edita's 2+2=5 (at some point you divide both sides by x-x in the proof But I couldn't come up with anything cool. I have seen a bunch of 1=2 proofs on the web though. So you can use those proofs to show 4=5 (by induction). Here's what someone had posted on the web a while back which proves 1=2:code:ln 2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/11 - 1/12 + ...-> 2ln 2 = 2 - 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5 + 2/11 - 1/6 ... = 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5 + 2/11 - 1/6 ... Now, collecting terms of equal denominator, we have: 2ln 2 = 1 - 1/2 + (2/3 - 1/3) - 1/4 + (2/5 - 1/5) - 1/6 + ... = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... = ln 2 Now, as ln 2 != 0, we can divide through by ln 2 to get: 2 = 1I still don't know where that proof goes wrong! Anyone have any ideas? Quote Link to comment Share on other sites More sharing options...
Harut Posted April 9, 2002 Author Report Share Posted April 9, 2002 Sip i think the problem is here. code:ln 2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 + 1/11 - 1/12 + ...-> 2ln 2 = 2 - 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5 + 2/11 - 1/6 ... = 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5 + 2/11 - 1/6 ...Now, collecting terms of equal denominator, we have:2ln 2 = 1 - 1/2 + (2/3 - 1/3) - 1/4 + (2/5 - 1/5) - 1/6 + ... = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... = ln 2Now, as ln 2 != 0, we can divide through by ln 2 to get:2 = 1the rith part of the first line is not equal to the line 6 because it has 2 times more terms that the line 6. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 9, 2002 Report Share Posted April 9, 2002 That is durty mathematic... and the most interesting part is hidden in the infinit... While you multiply the par numbers will be reduced, and since every odd numbers get the substraction in the ln fonction the reduction will lead that par numbers will get it, so you will have a substraction between the par reduced number and the odd number(of the same denominator) now by doing so you reduce the some of the series, so you will end up with this reduction of finding that ln 2 equal 2 ln 2, because this substraction reduce the some... Now by doing so, wierd are mathematic, you creat an invisable series on the infinit right sides, and this series get bigger more you go at your right side. Because the distance between the two numbers you substract, get bigger more you go at right, so at the infinit world, you will have a series that will be delimitated between the two substraction numbers. And since the series 2 ln 2 started with a par number, the par number is adventaged because the odd numbers end up with the (-) before them, and the some of the substraction between the par reduced number and the odd number will give a positive answer, then the series you created at the right infinit, is just the differences between the ln 2 and 2 ln 2, that is ln 2. It is possible to demonstrate it with series properties and sub-series isolation. I'll let this to Harut I think. [ April 09, 2002, 05:41 PM: Message edited by: Domino ] Quote Link to comment Share on other sites More sharing options...
Sip Posted April 17, 2002 Report Share Posted April 17, 2002 Domino + Harut ... thanks for the clarifications .. I thought it's about time to bring this thread back on top So ... I hope you haven't seen this before: http://home.earthlink.net/~Sip/misc/triangles.gif Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 17, 2002 Report Share Posted April 17, 2002 There is nothing misterious in this Seaphan, you cheated in this one. The two triangle do not have the same variation (y2-y1)/(x2-x1). One is 2/5 and the other 3/8, so in the first one, they are placed in order that the one(green) that has the highest variation is on top, and the lowest compleating the left side of the big triangle, so the real surface of the trianle is lower then a one of a base of 13u and a high of 5u, on the other hand when you change their places, and put the one with the lowest variation on top, you end up of doing the contrary you increase the surface, then in order to balance the difference of surface there is a hole of u*u that is left. Quote Link to comment Share on other sites More sharing options...
Azat Posted April 17, 2002 Report Share Posted April 17, 2002 huh? simpler answer. The dark red and the dark green are not true triangles because the top line is curved on them. The top is curved down and the top is curved up and the diff between the curves is that one cell that is missing. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 17, 2002 Report Share Posted April 17, 2002 Sorry Azat, they are true triangles. :-) Its the triangle that they form that is not a true one... the illusion that you have about the curves come from the fact that both triangles do not have the same angles, and for this the variations are not the sames. Read my answer above. :-) Quote Link to comment Share on other sites More sharing options...
Azat Posted April 17, 2002 Report Share Posted April 17, 2002 Oh God, First x-x is not zero and now they are true triangles. Take a straight edge and print that page and see if it is a straight line. The top line is curved down on one and up on the other. -------- Moderator talk: Harut you need to take care of Domino. I can't handle him no more. [ April 17, 2002, 11:07 AM: Message edited by: Azat ] Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 17, 2002 Report Share Posted April 17, 2002 Azat the big triangle is not a true one, the other little two are... they are not triangles of the same angle, this is why when you form the big one, it it like there is a curb, its not a curb, its two different lines, of different variation because the angles of each of these triangles are not the same. I am sure Harut will agree with me. Quote Link to comment Share on other sites More sharing options...
Azat Posted April 17, 2002 Report Share Posted April 17, 2002 Domino and Harut, you aguys are right. I had to look at the picture one more time to see what you were saying. Quote Link to comment Share on other sites More sharing options...
Harut Posted April 18, 2002 Author Report Share Posted April 18, 2002 Azat jan, i'm afraid but i have to disagree with you this time. the "hypathasis" of the two big "triangles" are composed of two straight lines, which do not form a straight line. so, the "triangles" don't have the same sureface area, because they are not the same in shape. even more, they are not triangles at all. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 18, 2002 Report Share Posted April 18, 2002 In more simple way, its what I said. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 18, 2002 Report Share Posted April 18, 2002 And to add, the two little triangles(green and red) are triangles. Quote Link to comment Share on other sites More sharing options...
Guest Fadi Posted April 19, 2002 Report Share Posted April 19, 2002 I was right like the x-x ? Quote Link to comment Share on other sites More sharing options...
Azat Posted April 25, 2002 Report Share Posted April 25, 2002 A small town had six soccer teams in last year's league, and each pair of teams played each other four times. At the end of the season, no two teams had won the same number of games. The 3rd, 4th, 5th, and last place teams had won 55%, 50%, 35%, and 30% of their games, respectively. How many games did the first place team win? Quote Link to comment Share on other sites More sharing options...
Harut Posted April 25, 2002 Author Report Share Posted April 25, 2002 14 Quote Link to comment Share on other sites More sharing options...
Sip Posted June 28, 2002 Report Share Posted June 28, 2002 Alright ... this thread has been quiet for too long This problem is more computer science-ish but I thought I'd put it here since it's also math: code:Can three houses be connected to three utilities without the pipes crossing? _______ _______ _______ | oil | |water| | gas | |_____| |_____| |_____| _______ _______ _______ |HOUSE| |HOUSE| |HOUSE| | one | | two | |three| |_____| |_____| |_____|So basically, the problem asks you to draw lines connecting the 3 houses to the 3 "utilities" without any lines crossing each other. Can you do it? Quote Link to comment Share on other sites More sharing options...
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