dms172 Posted September 19, 2008 Report Share Posted September 19, 2008 guess how many triangles there are? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 guess how many triangles there are? 90 There may be more, but I'm pretty confident there are at least that many. Quote Link to comment Share on other sites More sharing options...
0 dms172 Posted September 19, 2008 Author Report Share Posted September 19, 2008 There may be more, but I'm pretty confident there are at least that many.90 That's close but there's still more. This one's pretty hard Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 That's close but there's still more. This one's pretty hard 100 triangles Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 Wow you see 100 ?? i can only see 40 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 found 5 more so, 45 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 85 !! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 OK next time ill just wait and look very closely before i reply im now in 95 but if i find the 5 more for 100 i wont post it Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 OK sorry for these but had to cause i now see 105 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 I see 108. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted September 19, 2008 Report Share Posted September 19, 2008 I see 108. Doesn't the answer have to be a multiple of 5?60. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 Doesn't the answer have to be a multiple of 5? Sure, excuse me for seeing a 6 cornered star there. Now I say 100. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 Doesn't the answer have to be a multiple of 5?60. multiple of 5 is obviously necessary as there's rotational symetry order 5 (and 5 is prime - a six pointed star would not need a multiple of 6), but I can find 100. I drew them, but don't think I can get it to stay in a spoiler box Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 multiple of 5 is obviously necessary as there's rotational symetry order 5 (and 5 is prime - a six pointed star would not need a multiple of 6), but I can find I suggest that if it was a 6 pointed star, total count would need to be a multiple of 3, am I correct? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 (edited) multiple of 5 is obviously necessary as there's rotational symetry order 5 (and 5 is prime - a six pointed star would not need a multiple of 6), but I can find 100. I drew them, but don't think I can get it to stay in a spoiler box I think the second one in your first 5x row should actually be 10x. Also, I see one more configuration - it's basically a combination of that one and the second to last one from the first 10x row (I'll draw it later if I get a chance). This new one should be 10x as well. 115 Edited September 19, 2008 by Chuck Rampart Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 I think the second one in your first 5x row should actually be 10x. It's true, but in 10s, the second last one must be in 5s. Thus I had said 100. But now I realized that last one in 5s can be in 3 ways, not 5. My result is 98 now. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 (edited) I suggest that if it was a 6 pointed star, total count would need to be a multiple of 3, am I correct? I think that wouldn't quite be true, because you have a combination of triangles with 'symmetries'* of order 2, order 3 and order 6. So it might be a multiple of neither 2 nor 3! The easiest way to think of it is that you might find all the 3x and 6x triangles, then add on the "biggest" triangles, of which there are only two uniques, because they are equilateral. (* I call them symmetries, but they are actually a kind of combination of rotational and reflective non-symmetries - hmmm that doesn't really make sense!) I think the second one in your first 5x row should actually be 10x. Also, I see one more configuration - it's basically a combination of that one and the second to last one from the first 10x row (I'll draw it later if I get a chance). This new one should be 10x as well. I think you are right with the second in the 5x row - I was thinking that every triangle using a whole point would only have 5 rotations, but of course, this one also has a reflection for each. I'm intrigued by your new one - I still can't see it. Are you sure it is not just a rotation of the last in the top row? 105 Edited September 19, 2008 by foolonthehill Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 And I've just realised that the second to last in the top row has only 5 rotations! So that, 100 Basically, every triangle has 10 rotations, unless it also has a line of reflective symmetry which passes through the centre of the star, in which case it only has 5 Quote Link to comment Share on other sites More sharing options...
0 dms172 Posted September 19, 2008 Author Report Share Posted September 19, 2008 First of all let me say congrats cuz the the source where i got this didn't even find 100 many so after a carefully recount I'm pretty sure there's 100 triangles, but if u can find more for sure then plz post picture and prove me wrong. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 First of all let me say congrats cuz the the source where i got this didn't even find 100 many so after a carefully recount I'm pretty sure there's 100 triangles, but if u can find more for sure then plz post picture and prove me wrong. 100 was OK for me, but as I wrote before, at foolonthehill's nice picture, third of 5x triangles (they are the largest triangles) can occur only tree times. Am I wrong? This also eliminates Bonanova's suggestion as it must be a multiply of 5??? I still suggest 98. Quote Link to comment Share on other sites More sharing options...
0 dms172 Posted September 19, 2008 Author Report Share Posted September 19, 2008 count again there's 5 of those largest triangles Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 count again there's 5 of those largest triangles Sorry, you're right 100 is correct. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 19, 2008 Report Share Posted September 19, 2008 I'm intrigued by your new one - I still can't see it. Are you sure it is not just a rotation of the last in the top row? Agreed, it was a duplicate. My bad. Quote Link to comment Share on other sites More sharing options...
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dms172
guess how many triangles there are?
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