bonanova Posted March 2, 2009 Report Share Posted March 2, 2009 I have some golf balls, some identical coins, and some pencils. I want to place them on a table in groups so that each object touches all the others in that group. How large can the group be, in each case? Note there are three answers here. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 (edited) 4 in each case Edited March 2, 2009 by scarecrow Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 2, 2009 Author Report Share Posted March 2, 2009 1 out of 3. That's a start ... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I want to place them on a table in groups so that each object touches all the others in that group. First I have to know whether they are placed on a plane or in a space? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 2, 2009 Author Report Share Posted March 2, 2009 They are in the space directly above the table. They do not all need to contact the table: they may be stacked. Is that what you are asking? Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted March 2, 2009 Report Share Posted March 2, 2009 (edited) You thought four was cool? Well guess what, I can do it with 2. And 3. You've been pwned. Also, Bona, man was I happy to see some new riddles from you today. Edited March 2, 2009 by Izzy Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 Also, Bona, man was I happy to see some new riddles from you today. You thought four was cool? Well guess what, I can do it with 2. And 3. You've been pwned. haha, I was going to say the same thing. But I grabbed a pile of pencils (actually pens) and fiddled around for a while until I found a configuration to have all 5 of them all touching the four others simultaneousley. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 well it seems to me that the coins can go to 5, and the golfballs can go to four. Not sure on the pencils. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 Four balls, three on the table all touching in a triangle, one on top in the middle of that triangle to touch the other three. The coins will be basically the same configuration, just easier to accomplish as they won't roll away. The pencils you can do a couple different ways. You can place three of them in a triangle, end to end, then carefully place the fourth from one of the angles (touching two pencils) to somewhere along the length of the third pencil. You can also do the pencils in the same fashion as the coins and golf balls, but you'd have to have some pretty steady hands. I would love to see a description of DanCDow's 5 pencil solution. I can't seem to visualize it, myself. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I took the time to draw in 3d the 5 pencil arrangement. This arrangement came about as a fluke. Since the pens I used were not exactly identical, this may not work in a perfect world. But who says we're in a perfect world, right? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 But it doesn't work. You can lay out three pencils in a sort of "Y" shape so that they all touch each other, similar to the coins. Now lift the point where they come together and place a pencil underneath. The mistake is that one would now believe that if you place a pencil on top of that point parallel to the one on the bottom, that they would all touch each other. Unfortunately, the angle necessarry for the top and bottom pencils to touch would create the slightest gap between the top pencil and the one furthest away from where the top and bottom meet. It worked with my pens, but they have textured, curvy grips that allow them all to touch. Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 2, 2009 Report Share Posted March 2, 2009 here's Rookie's answer to the pencil one seven Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 But it doesn't work. You can lay out three pencils in a sort of "Y" shape so that they all touch each other, similar to the coins. Now lift the point where they come together and place a pencil underneath. The mistake is that one would now believe that if you place a pencil on top of that point parallel to the one on the bottom, that they would all touch each other. Unfortunately, the angle necessarry for the top and bottom pencils to touch would create the slightest gap between the top pencil and the one furthest away from where the top and bottom meet. It worked with my pens, but they have textured, curvy grips that allow them all to touch. I think I see what you are saying, like I said... who says we're in a perfect world? I say it works because of the curvy grips (I have similar "imperfections" on my pens)! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 here's Rookie's answer to the pencil one seven Alas, I forgot about that one. The great thing about a failing memory is that you can be impressed by the same thing over and over again! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 ...5? (4 in a square, 1 on top) Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted March 2, 2009 Report Share Posted March 2, 2009 Also, Bona, man was I happy to see some new riddles from you today. You thought four was cool? Well guess what, I can do it with 2. And 3. You've been pwned. Oh, pfft, I totally thought it was all meant to be one large group, i.e. three balls touching, with three coins touching, each touching each other, and then three pencils touching, each touching each of the balls and coins. Which looking back doesn't exactly work, but it did in my head this morning. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I still do not know how to insert a spoiler, but I think each group can be 5 items. I have some golf balls, some identical coins, and some pencils. I want to place them on a table in groups so that each object touches all the others in that group. How large can the group be, in each case? Note there are three answers here. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 2, 2009 Author Report Share Posted March 2, 2009 here's Rookie's answer to the pencil one seven Thanks PT, and a tip of the hat rookie! Wolfram has it for "cylinders". Of course I searched on pencils and cigarettes, but forgot to search for matchsticks!!! I think we're agreed now on the pencils and the golf balls. Are we agreed on the coins? Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted March 3, 2009 Report Share Posted March 3, 2009 Yeah, agreed. I can't seem to get past 5. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 3, 2009 Report Share Posted March 3, 2009 Yeah, agreed. I can't seem to get past 5. Please explainI can't get past 4. By adding the fifth coin, I invariably separate two of the coins. Please describe the 5 coin solution? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 3, 2009 Report Share Posted March 3, 2009 Thanks PT, and a tip of the hat rookie! Wolfram has it for "cylinders". Of course I searched on pencils and cigarettes, but forgot to search for matchsticks!!! I think we're agreed now on the pencils and the golf balls. Are we agreed on the coins? but they do not work in the way the pencils do. I've tried several configurations to try and fit a fifth coin in, and each time it ends up with at least one of the coins being separated from one of the others. I'm going to stand at four coins. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 5, 2009 Author Report Share Posted March 5, 2009 but they do not work in the way the pencils do. I've tried several configurations to try and fit a fifth coin in, and each time it ends up with at least one of the coins being separated from one of the others. I'm going to stand at four coins. leaning two of them. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 5, 2009 Report Share Posted March 5, 2009 (edited) I can only get 5. If you stand 3 coins on their edge touching, they will hold up one coin laying on top. Put one more coin along the edges of the 3 and it will touch the top coin also. Edited March 5, 2009 by DforDumb Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 5, 2009 Report Share Posted March 5, 2009 You could also make 4 stand on their edges in the 4 cardinal directions. Like a compass points N, E, S, W, stand 4 coins in that position, 4 tips are touching, then lay one more on top. Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 5, 2009 Report Share Posted March 5, 2009 You could also make 4 stand on their edges in the 4 cardinal directions. Like a compass points N, E, S, W, stand 4 coins in that position, 4 tips are touching, then lay one more on top. I don't think that will work. Only three coins standing on edge can touch like that. Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted March 5, 2009 Report Share Posted March 5, 2009 I don't think that will work. Only three coins standing on edge can touch like that. if corner to corner is good enough, you could offset each coin by half it's width to get rid of the center square. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
I have some golf balls, some identical coins, and some pencils.
I want to place them on a table in groups so that each object touches all the others in that group.
How large can the group be, in each case?
Note there are three answers here.
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