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 Guest Posted January 15, 2009 Report Share Posted January 15, 2009 8? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2009 Report Share Posted January 15, 2009 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...This inspired me an other simple question: In 3d, what is the formula that gives the count of angles which are constructed by n number of matches (or lines), those intersect at a unique point (for instance as O point in xyz analitic diagram)? I hope I worded it thoroughly. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 15, 2009 Author Report Share Posted January 15, 2009 This inspired me an other simple question: In 3d, what is the formula that gives the count of angles which are constructed by n number of matches (or lines), those intersect at a unique point (for instance as O point in xyz analitic diagram)? I hope I worded it thoroughly. As you word it, N appears to have 3 as upper limit; and that has been solved. One might ask for N>3, but physical matches can't supply a verification. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2009 Report Share Posted January 15, 2009 As you word it, N appears to have 3 as upper limit; and that has been solved. One might ask for N>3, but physical matches can't supply a verification. I should have impressed that in my question the angles have not to be right angles!!! Quote Link to comment Share on other sites More sharing options...
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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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