bonanova Posted January 13, 2009 Report Share Posted January 13, 2009 If I arrange four matches perpendicularly end to end, [forming a square] I make four right angles. If I move parallel matches inward, pairwise, [making a # figure - tic-tac-toe] I make sixteen right angles. How many right angles can be made from just three matches? Quote Link to comment Share on other sites More sharing options...
0 HoustonHokie Posted January 13, 2009 Report Share Posted January 13, 2009 (edited) 8 --|-- --|-- | | Edited January 13, 2009 by HoustonHokie Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 eight. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 12. Think three dimensionally. Make a cross with two matches and then put the third perpendicular to both (creating a set of three dimensional axes). Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 If I arrange four matches perpendicularly end to end, [forming a square] I make four right angles. If I move parallel matches inward, pairwise, [making a # figure - tic-tac-toe] I make sixteen right angles. How many right angles can be made from just three matches? From the above layout, removal of 1 match stick will leave 8 right angles with the three remaining sticks. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 (edited) 12 Edited January 13, 2009 by xucam Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 (edited) Eight Edited January 13, 2009 by Nin0br0wnx76 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 12 I think this teaser is written under the assumption that we are working within a single plane... but i'm not sure. if not then your answer appears correct. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 13, 2009 Report Share Posted January 13, 2009 12. Think three dimensionally. Make a cross with two matches and then put the third perpendicular to both (creating a set of three dimensional axes). Agreed. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 I'd say that, assuming it is in one plane, that it would be 8. With 2 matches, we'd have 4 right angles; with 4 matches, we'd have 16 right angles. So, assuming this is all in one plane again, we'd have 2^(number of matches), being 3 in this case, so 8 right angles. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 I'd say that, assuming it is in one plane, that it would be 8. With 2 matches, we'd have 4 right angles; with 4 matches, we'd have 16 right angles. So, assuming this is all in one plane again, we'd have 2^(number of matches), being 3 in this case, so 8 right angles. (spam/ ahh, every riddle I get to is already answered..stupid time restrictions.) I agree. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 I'd say that, assuming it is in one plane, that it would be 8. With 2 matches, we'd have 4 right angles; with 4 matches, we'd have 16 right angles. So, assuming this is all in one plane again, we'd have 2^(number of matches), being 3 in this case, so 8 right angles. I also agree Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 I'd say that, assuming it is in one plane, that it would be 8. With 2 matches, we'd have 4 right angles; with 4 matches, we'd have 16 right angles. So, assuming this is all in one plane again, we'd have 2^(number of matches), being 3 in this case, so 8 right angles. I don't think that you can assume that since the original transform was described as being in a single plane, that the answer to the riddle should be so constrained. (given that match sticks have width, the tic-tac-toe arrangement is not really in a single plane) I think that going from the square to tic-tac-toe in a single plane was a red herring, to keep people from thinking about a more novel solution. 'How many can you make' implies that the riddle seeks the highest number that can be made from three matches.The problem is trivial if confined to a single plane. 8 is not the most you can make with 3 matches. 12 is. Unless you split each match down the middle, and ... Quote Link to comment Share on other sites More sharing options...
0 Jiminy Cricket Posted January 14, 2009 Report Share Posted January 14, 2009 If I arrange four matches perpendicularly end to end, [forming a square] I make four right angles. If I move parallel matches inward, pairwise, [making a # figure - tic-tac-toe] I make sixteen right angles. How many right angles can be made from just three matches? Since you did not specify they have to be laying down, I'd say 12. Put one vertical and two horizontal. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 I dunno... I can get you 8 right angles out of two match sticks...and 24 from three. Wet the matches thoroughly, and bend them to fit the outside of a sphere, so that the ends touch on the opposite side. Now you have 4 right angles where they cross, and another four right angles where they touch on the other side. Now stick a third matchstick through the middle (sticking out both 'poles'), and you'll add another 16 right angles, for a total of 24. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 it does not says the match sticks are straight. I can have a zig zak match sticks with 90 degree angles and make as many right angles as i want \/\/\/\/\/\/\/\/\/\/\/\/\/\/ --- match stick 1 /\/\/\/\/\/\/\/\/\/\/\/\/\/\ --- match stick 2 \/\/\/\/\/\/\/\/\/\/\/\/\/\/ --- match stick 3 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 0. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 it does not says the match sticks are straight. I can have a zig zak match sticks with 90 degree angles and make as many right angles as i want \/\/\/\/\/\/\/\/\/\/\/\/\/\/ --- match stick 1 /\/\/\/\/\/\/\/\/\/\/\/\/\/\ --- match stick 2 \/\/\/\/\/\/\/\/\/\/\/\/\/\/ --- match stick 3 You can bend a matchstick that many times? I'd think the wooden ones would break, and the paper ones would just fall apart. Seriously...I'd think I could get about 5 right angles max out of a single matchstick, if I had needle nose pliers and a few minutes. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 If I arrange four matches perpendicularly end to end, [forming a square] I make four right angles. If I move parallel matches inward, pairwise, [making a # figure - tic-tac-toe] I make sixteen right angles. How many right angles can be made from just three matches? 12. you need 3D Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 The problem with saying 12 is that the OP states that the max is 16 with 4, can you not create more that 16 right angles in three dimensions with 4 sticks? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 The problem with saying 12 is that the OP states that the max is 16 with 4, can you not create more that 16 right angles in three dimensions with 4 sticks? The OP said that if they took the square formation and moved to the tic-tac-toe then you got 16 - not that that was a maximum/ Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 (edited) The problem with saying 12 is that the OP states that the max is 16 with 4, can you not create more that 16 right angles in three dimensions with 4 sticks? Actually...I'm not sure you can, not with the sticks still straight in all three dimensions. I have no proof for that, just an intuition. I'd be interested in someone showing that 4 straight sticks in 3D could give more than 16. Something other than my solution above of wrapping the sticks around a spherical surface. Edit: Of course, the more dimensions you add, the more right angles you could have. Placing another stick in an additional dimension could give you three sticks all at right angles to each other in the XYZ grid, and a fourth stick at right angles to them all in the other dimension Edited January 14, 2009 by brotherbock Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 The problem with saying 12 is that the OP states that the max is 16 with 4, can you not create more that 16 right angles in three dimensions with 4 sticks? Assuming we stay in three dimensional space (which, of course, matchsticks exist in), then no actually. I was thinking about this myself earlier and wondering if there is any formula for right angles given n matchsticks. I got as far as 3 matchsticks gives 12, 4 gives 16, 5 gives 24, 6 gives 32 and then, not having a piece of paper, decided to stop before I got a headache. I don't think there is a formula, but would be interested if anyone can show one... Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted January 14, 2009 Report Share Posted January 14, 2009 (edited) 6 matchsticks in 2D yields 36. Edited January 14, 2009 by Prof. Templeton Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 (edited) Assuming we stay in three dimensional space (which, of course, matchsticks exist in), then no actually. I was thinking about this myself earlier and wondering if there is any formula for right angles given n matchsticks. I got as far as 3 matchsticks gives 12, 4 gives 16, 5 gives 24, 6 gives 32 and then, not having a piece of paper, decided to stop before I got a headache. I don't think there is a formula, but would be interested if anyone can show one... Eh, I still say 2 sticks gives 8, 3 sticks gives 24, 4 sticks gives...(adding)...40, 5 sticks gives 56, and possibly etc. With the matchsticks wrapped around or sticking through a sphere. Edited January 14, 2009 by brotherbock Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 14, 2009 Report Share Posted January 14, 2009 infinite! in theory, W&T or decomp etc How many times can you take 2 from 32.... before you loose count Quote Link to comment Share on other sites More sharing options...
Question
bonanova
If I arrange four matches perpendicularly end to end, [forming a square] I make four right angles.
If I move parallel matches inward, pairwise, [making a # figure - tic-tac-toe] I make sixteen right angles.
How many right angles can be made from just three matches?
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