What is the maximum number of triangles you can form by drawing three triangles on a piece of paper?
Good luck!
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Sign up to join this communityWhat is the maximum number of triangles you can form by drawing three triangles on a piece of paper?
Good luck!
I've managed to get
30 triangles
As follows
The trick here is
To make the three triangles maximally intersecting. I'm not sure if this is optimal here though.
Counting
Note here that each red kite region as shown yields two large triangles and two small triangles. Going around the outer vertices we see that the large triangles are distinct so there are 18 of them but the small triangles are each counted twice so there are 9 of them and then we add the three original triangles to get 30.
This might not be optimal, but its the best one I could find:
It has 18 triangles.
here are some of the triangles highlighted for clarity
and then, of course, the 3 original triangles.
Every larger distinct triangle has a side with a different colour and a number adjacent to that triangle. The smaller distinct triangles have a number inside them, except in cases where the triangle is very small, in which case the number is adjacent to the triangle. The three overlapping triangles generate twenty-four distinct triangles.