Thelema Posted May 4, 2009 How many coins of diametre 1cm can you pack into a 10cm by 10cm square? The answer may surprise you! I should offer a prize to the right answer... Share this post Link to post Share on other sites
ThunderIdeal Posted May 4, 2009 (edited) 108, 117 , 126, 135 or 144. stupidly basic attempt at the problem don't keep us hanging too long. Edited May 4, 2009 by ThunderIdeal Share this post Link to post Share on other sites
obtuse Posted May 4, 2009 100... surely. trick question? Share this post Link to post Share on other sites
ThunderIdeal Posted May 4, 2009 nah mathematicians are always working on this sort of problem, sometimes they have only established that the maximum is between two given numbers, but haven't established what that number is for certain. i dunno, euclidean geometry has sorta been done to death and isn't really where it's at anymore, but that doesn't mean we have all of the answers. Share this post Link to post Share on other sites
MORG Posted May 4, 2009 Depends how high you can stack em. Share this post Link to post Share on other sites
Freaky Chicken Posted May 4, 2009 my second guess is 125, assuming it is 2D. Share this post Link to post Share on other sites
Thelema Posted May 4, 2009 ok obvious first response is to stack in 10 rows of 10, making 100. but how about if you stacked them 10, 9, 10 ..."cigarette style" in between each other, then you can squish an 11th row in! Making 105 coins. Ah, but the optimal solution is 106 coins. Can you see how? Share this post Link to post Share on other sites
Alice Posted May 4, 2009 Ah, but the optimal solution is 106 coins. Can you see how? Can I use a hacksaw? Share this post Link to post Share on other sites
gerbil Posted May 4, 2009 Initially not particularly interested in the exact figure off the top of the head, as a vague guess based on roundness i went for 110, 'can you see how', I think so, based on roundness. Share this post Link to post Share on other sites
JDanger Posted May 4, 2009 (edited) I was going to ask "How thick are the coins?", but then I realised it was a simple 10x10 square, not a 10x10x10 cube. In that case, surprise me. Edited May 4, 2009 by JDanger Share this post Link to post Share on other sites
gromit Posted May 4, 2009 CBF actually doing it, but what if you put a coin in the middle, then circled it in more coins, then circled that with more coins etc...Would that make a difference? Share this post Link to post Share on other sites
Fenris Posted May 4, 2009 If the coins can be stacked end on ie on their sides, I imagine quite a few. Tessellation http://en.wikipedia.org/wiki/Tessellation Share this post Link to post Share on other sites
MindExpansion Posted May 4, 2009 Depends how high you can stack em. Was going to say the very same thing. Share this post Link to post Share on other sites
ThunderIdeal Posted May 4, 2009 thelema has already said the answer is 106. challenge now is to figure out how to fit 106. Share this post Link to post Share on other sites
J Smith Posted May 4, 2009 (edited) Edit: Answer removed as spoiler tag didn't work Edited May 4, 2009 by madhouses visites Share this post Link to post Share on other sites
ThunderIdeal Posted May 4, 2009 would have been so good if somebody figured that out with their own mind. good thread. Share this post Link to post Share on other sites
J Smith Posted May 4, 2009 I guess that was directed at me. Just because I posted a pic doesn't mean I didn't work out the solution. Anyways, I've removed the pic so that other people have an opportunity to work it out themselves. Sorry to ruin the post by answering the question!! Share this post Link to post Share on other sites
watertrade Posted May 5, 2009 its a good question I like. I once had to figure out how many spheres fit into a cube - similar idea in 3D. if your interested look up the Kepler Problem. interesting stuff. Share this post Link to post Share on other sites
ThunderIdeal Posted May 5, 2009 madhouse, i didn't mean to say you ruined it, but you do have better googling skills than myself. it's not a ridiculously difficult solution given the clues that thelema has already given. should just require a bit of thought and rough hand drawn diagram. interesting to note that with random packing of spheres (eg, fitting them tightly but not within a particular shape) the best configuration was thought to be discovered centuries ago by somebody, maybe kepler, but a 20th century geometer discovered a better configuration. Share this post Link to post Share on other sites
santiago Posted May 5, 2009 (edited) I might go the other way and say that for some geometric reason circles take up a tiny fraction more space, its a complete guess with no logic at all but im going 99. Ahh bugger the answer was 106, i didnt catch the result was already given : ) Edited May 5, 2009 by santiago Share this post Link to post Share on other sites
~shameless~ Posted May 5, 2009 That was a good one Thelema, Share this post Link to post Share on other sites
J Smith Posted May 5, 2009 I admit I did google that pic after I worked it out. You are right TI, the hints given does make it easier. I wouldn't have got it without Thelema's hints. Spoiler follows... Assuming the maximum number of columns is 11, and columns can be 10 or 9 coins high, it means that there must be 4 columns of 9 coins (=36) and 7 columns of 10 coins (=70). I'm sure there is a more mathematically complex solution based on pi or pie or psy or some such thing. Nice question Thelema Share this post Link to post Share on other sites