Sip Posted June 28, 2002 Report Share Posted June 28, 2002 quote:Originally posted by Harut:what is K3,3 planar?A "graph" in graph theory is basically a bunch of points connected by a bunch of lines (edges). It has no real geometrical meaning of physical dimensions. It's more of an "abstract" structure. the K3,3 is basically the name of the graph which is in the problem above. A group of 3 points connected to another group of 3 points (all connections between groups). A graph is planar if it's edges can be drawn on a plane (flat surface) without anything crossing each other. The one above is NOT planar since you can't draw all the lines so that they don't cross. There are 2 basic graphs that are not planar: K3,3 (you already saw above)K5 (put 5 points on a paper and connect all together) I think there is a theorem somewhere that says any non planer graph must have at least one of those 2 smaller graphs as a sub component (it's been a while since my last graph theory class so I am a bit shaky on this ) There is a pretty interesting and easy to understand version of the proof for K3,3 which I'll try to remember... It all sounds complicated but as you see, it's NOT!!! Even a kid at the age of 5 can grasp the ideas. That's what I really love about these "computer science" type stuff Quote Link to comment Share on other sites More sharing options...
Harut Posted June 28, 2002 Author Report Share Posted June 28, 2002 Sip jan, i've been thinking over this problem since i was 5 years old. unless, let's say, the oil pipe goes through H1---H2---H3 there is no way. what i mean is thiscode: O ----- W ----- G ------ | / | | | | / | | | |/ | | | H1--------H2--------H3 | | |_____________| | |__________________________| Quote Link to comment Share on other sites More sharing options...
Sip Posted June 28, 2002 Report Share Posted June 28, 2002 Wow! You learned about the K3,3 graph when you were 5 ???!!!! I'm impressed Yes, your answer is correct. The K3,3 is the smallest graph which is NOT planar (it's lines cannot be drawn in a plane). Now the interesting question ... can you PROVE your answer? Quote Link to comment Share on other sites More sharing options...
Harut Posted June 28, 2002 Author Report Share Posted June 28, 2002 quote:Originally posted by Sip:Wow! You learned about the K3,3 graph when you were 5 ???!!!! I'm impressed no, i just had a relative who liked to give me all kinds of wiard problems with no solutions, then offer a kandy or money if i solved them in 15 days. quote:Yes, your answer is correct. The K3,3 is the smallest graph which is NOT planar (it's lines cannot be drawn in a plane).what is K3,3 planar? quote:Now the interesting question ... can you PROVE your answer?sure, take your pencil and paper and draw all the possible lines. eventually you will come to that conclusion. Quote Link to comment Share on other sites More sharing options...
Sip Posted July 23, 2002 Report Share Posted July 23, 2002 If you have some free time, try to figure out this sequence! I spent some time on it but just couldn't figure it out. But I do know the answer now 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ... Just make sure you have a lot of free time Quote Link to comment Share on other sites More sharing options...
Azat Posted August 7, 2002 Report Share Posted August 7, 2002 A fool wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbour, also a fool, wants to do the same only he wants the rope on sticks 1 meter above the ground. How much more rope does he need?-------- I am affraid that Harut is going to solve this really fast and make me look like the fool. Quote Link to comment Share on other sites More sharing options...
Azat Posted August 7, 2002 Report Share Posted August 7, 2002 Who took the candy bar?During the lunch hour at school, a group of five boys from Miss Sulamita home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:1. Azat: "Neither Sip nor I did it." 2. Harut: "It was Azat or Domino." 3. Domino: "Both Azat and Harut are lying." 4. Movses: "Domino's statement is not true; one of them is lying and the other is speaking the truth." 5. Sip: "What Movses said is wrong." When Miss Sulamita was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Sulamita is correct, can you determine who took the candy bar? Quote Link to comment Share on other sites More sharing options...
Sip Posted August 7, 2002 Report Share Posted August 7, 2002 quote:Originally posted by Azat:Who took the candy bar?I expect behavior like that from Domino ... but Movses ... shame on you for lying Bayts Azat, desnum es Harut e inchpes shut mexke ketsum e ko vren? .... and thanks for sticking up for me! [ August 07, 2002, 03:39 PM: Message edited by: Sip ] Quote Link to comment Share on other sites More sharing options...
MosJan Posted August 7, 2002 Report Share Posted August 7, 2002 quote:Originally posted by Azat:Who took the candy bar?During the lunch hour at school, a group of five boys from Miss Sulamita home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:1. Azat: "Neither Sip nor I did it." 2. Harut: "It was Azat or Domino." 3. Domino: "Both Azat and Harut are lying." 4. Movses: "Domino's statement is not true; one of them is lying and the other is speaking the truth." 5. Sip: "What Movses said is wrong." When Miss Sulamita was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Sulamita is correct, can you determine who took the candy bar?yes matov chem kpel - Ashotna arel - yerb duq tan@ cheq dzer knoj het - L Alla Quote Link to comment Share on other sites More sharing options...
Azat Posted August 8, 2002 Report Share Posted August 8, 2002 quote:Originally posted by Sip:If you have some free time, try to figure out this sequence! I spent some time on it but just couldn't figure it out. But I do know the answer now 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ... Just make sure you have a lot of free time smilies/lol.gifI know the answer to this one as well only because a friend had to tell me the answer. I think it is one of those questions that you can spend hours and hours and hours and not even be close. Quote Link to comment Share on other sites More sharing options...
nairi Posted August 8, 2002 Report Share Posted August 8, 2002 Math is my worst subject, and I'm probably completely wrong, but I'm willing to give this sequence a try: ...30 31 36 37 39 40 54 55 57 58 63 64 66 67 81 82 84 85 90 91 93 94 108 109... I'm wondering, is this one of those really difficult ones that look simple or one of those really simple ones that look difficult? Nairi Quote Link to comment Share on other sites More sharing options...
Harut Posted August 8, 2002 Author Report Share Posted August 8, 2002 wow, three new problems to solve! Quote Link to comment Share on other sites More sharing options...
Sip Posted August 8, 2002 Report Share Posted August 8, 2002 quote:Originally posted by nairi:Math is my worst subject, and I'm probably completely wrong, but I'm willing to give this sequence a try: ...30 31 36 37 39 40 54 55 57 58 63 64 66 67 81 82 84 85 90 91 93 94 108 109...If math is one of your "worst" subjects, I can't imagine how you are in one of the "better" subjects!!! That is actually a pretty cool answer . Even though it is NOT the one I had in mind (I don't know what Azat has in mind), I think that is a perfectly valid answer as far as I can tell! Wow The original sequence I had in mind jumps from 40 to 81 ... so it goes: 37 39 40 81 82 84 Quote Link to comment Share on other sites More sharing options...
nairi Posted August 9, 2002 Report Share Posted August 9, 2002 Does this make sense? ...31 36 37 39 40 81 82 84 85 90 91 93 94 108 109 117 118 120 121... Nairi Quote Link to comment Share on other sites More sharing options...
Sip Posted August 9, 2002 Report Share Posted August 9, 2002 quote:Originally posted by nairi:Does this make sense? ...31 36 37 39 40 81 82 84 85 90 91 93 94 108 109 117 118 120 121... NairiIt makes sense if there is a 111 112 between 109 and 117. I think you have found "a pattern" which works in the beginning for what I started the problem with. But if we keep going, you are going to miss the BIG jumps! It's not a fault of the solution, it's just that to really see the pattern, we need to go much farther in the sequence. In any case, it's a strange problem to begin with. I only put it here since I wasted so much time on it and I figured it's only fair to let others do the same So I am guessing that you have noticed there is basically a repeating "+1, +2, +1", with jumps of +5, +14, +5 ... But then we got a +41 (between 40 and 81) and soon there is a +122 jump! i.e. the pattern goes: 111 112 117 118 120 121 243 244 246 ... So, if you and I are synced so far, the problem is where those "jumps" take place and try to predict the next one! Although there IS an explanation for this pattern. Quote Link to comment Share on other sites More sharing options...
nairi Posted August 9, 2002 Report Share Posted August 9, 2002 Okay, how about this? ...94 108 109 111 112 117 118 120 121 243 244 246 247 252 253 255 256 270 271 273 274 279 280 282 283 567 568 570 571 576 577... Nairi Quote Link to comment Share on other sites More sharing options...
MosJan Posted August 9, 2002 Report Share Posted August 9, 2002 knereq sxal ter mta es im ter@ chi voch $$$ ka voch el grram kam CArrat - Karrat Quote Link to comment Share on other sites More sharing options...
nairi Posted August 9, 2002 Report Share Posted August 9, 2002 I knew it couldn't be as easy as it looked, esp. if you (math-brains) spent a day trying to figure it out. Thanks for the solution. It was an interesting endeavor. Nairi Quote Link to comment Share on other sites More sharing options...
nairi Posted August 9, 2002 Report Share Posted August 9, 2002 Seaphan, do these patterns make sense to you (in the difference)? I'm wondering, what comes before pattern a)? Hint? I'm really enjoying this. a) 1 .. 1 .. 1 .. 1 .. 1 .. 1x3-1=22x3-1=5 2 5 2 ... 2 5 2 ... 2 5 2 ... c) 5x3-1=1414x3-1=41 14 41 14 ... 14 41 41 ... 14 41 14 ... d) 41x3-1=122 122x3-1=365 122 365 122 .... 122 365 122 .... 122 365 122 ... e) 365x3-1=10941094x3-1=3281 1094 3281 1094 ..... 1094 3281 1094 ..... 1094 3281 1094 ... f) 3281x3-1=98429842x3-1=29525 9842 29525 9842 ........ 9842 29525 9842 ....... 9842 29525 9842 ....... etc. Nairi [ August 09, 2002, 07:46 AM: Message edited by: nairi ] Quote Link to comment Share on other sites More sharing options...
Sip Posted August 9, 2002 Report Share Posted August 9, 2002 quote:Originally posted by nairi:I knew it couldn't be as easy as it looked, esp. if you (math-brains) spent a day trying to figure it out. Thanks for the solution. It was an interesting endeavor. Well, I for one didn't even realize the pattern that you found ... the "description" of the solutions is: All binary integers, assumed to be in base 3, converted to decimal. I think one may realize this pattern if that person notices the jumps happen at powers of 3 (1 3 9 81 243 ...) but I for one didn't. So the pattern is: 1 10 11 100 101 110 111 1000 ... which converted from base 3 to decimal (base 10) are: 1 3 4 9 10 12 13 27 ... -------Edit: Don't know about you guys but sometimes I really need to focus and think about something completely unrelated to what I am doing in order to get "unstuck" on a problem (talking about a real problem that I may be working on). Has it ever happened that you are thinking hard about something, you don't seem to be ANYWHERE near the answer after several hours, and then you go do something else, like watch tv, eat, do laundry, or just check something like hyeforum for a few minutes, and all of a sudden the answer hits you? It's strange. But happens to me a lot ... even several times when I have been asleep. I think it is very strange how the thought process works in humans [ August 09, 2002, 07:56 AM: Message edited by: Sip ] Quote Link to comment Share on other sites More sharing options...
nairi Posted August 9, 2002 Report Share Posted August 9, 2002 quote:Originally posted by Sip:I think one may realize this pattern if that person notices the jumps happen at powers of 3 (1 3 9 81 243 ...) but I for one didn't.Told you. The less you know the smarter you get. You're thinking too complex. I only know how to add, subtract, multiply and divide. There's not much you can experiment with that. Nairi Quote Link to comment Share on other sites More sharing options...
Harut Posted August 9, 2002 Author Report Share Posted August 9, 2002 quote:Originally posted by Azat:A fool wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbour, also a fool, wants to do the same only he wants the rope on sticks 1 meter above the ground. How much more rope does he need?-------- I am affraid that Harut is going to solve this really fast and make me look like the fool.hey you fool. if it's just the matter of increase the radius by 1 m then the second fool needs some 6-7 meter more rope. but if it's not that, then how many sticks are there? how far are they apart? is the ground "flat" all the way around the globe? can we somehow "dzqel" the rope? and so on... Quote Link to comment Share on other sites More sharing options...
Harut Posted August 9, 2002 Author Report Share Posted August 9, 2002 quote:Originally posted by Azat:Who took the candy bar?During the lunch hour at school, a group of five boys from Miss Sulamita home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:1. Azat: "Neither Sip nor I did it." 2. Harut: "It was Azat or Domino." 3. Domino: "Both Azat and Harut are lying." 4. Movses: "Domino's statement is not true; one of them is lying and the other is speaking the truth." 5. Sip: "What Movses said is wrong." When Miss Sulamita was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Sulamita is correct, can you determine who took the candy bar?Fadin estegh chi, inch ases glxin sarqum es, ha? te hents candyn arel u paxel a? Quote Link to comment Share on other sites More sharing options...
Harut Posted August 9, 2002 Author Report Share Posted August 9, 2002 oops, i posted the above message, and then noticed that Sip had already answered. Quote Link to comment Share on other sites More sharing options...
Sip Posted August 9, 2002 Report Share Posted August 9, 2002 quote:Originally posted by nairi:Okay, how about this? ...94 108 109 111 112 117 118 120 121 243 244 246 247 252 253 255 256 270 271 273 274 279 280 282 283 567 568 570 571 576 577...Hmmmmm ... sorry Here are the first 1000 numbers in the sequence: seq.txt.Here are the first 1000 differences between sequential numbers: diff.txt. Here are the 'C' source files for the simple programs I used to generate the above files. Note that these are basically "solutions" if you can figure out what I did! So look as a last resort. Harut ... you may like this Generate the sequence: seq.cpp.Generate the differences: diff_src.txt. [ August 09, 2002, 12:32 AM: Message edited by: Sip ] Quote Link to comment Share on other sites More sharing options...
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