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Puzzle #9 – Shape Puzzles – Triangles

I ran into Isosceles. He had a great idea for a new triangle! Woody Allen

“I ran into Isosceles. He had a great idea for a new triangle!”
Woody Allen

It’s been some time since my last post. I was overcome by events, but now I’m back. Today is a relatively easy set of puzzles. However, beware! These are counting shape puzzles, where the shape is always a triangle. Just count the number of triangles. Pretty simple, but oddly enough most people miss the first puzzle. So here goes, how many triangles are in the following image.

2014Jul21-1Many people say “2”, the triangle on the left and the triangle on the right.  But really there are three triangles, the left, right and the big triangle (made up of both of them).  Well if you missed that here’s another chance, how many triangles can you count in the following image?


Essentially this figure is the right-side triangle from the first figure, with two lines added.  In all, there are five triangles.  Look again if you didnt count five.  Let’s reflect this figure about the vertical side to generate the next figure.  Essentially, we just “doubled” the second figure to make the third figure.  How many triangle can you count?  Is it twice as many as in the second figure?


Although the second figure was doubled (via reflection) to make the third figure, the number of triangles more than doubled.  The number of triangles in the third figure is thirteen.  Now let’s make the fourth figure by removing the center line from the third figure.  How many triangles can you count?


The number of triangles in the fourth figure is five, just like in the second figure.  Again, a straight forward puzzle that is often missed.

Good luck with the puzzles and pass them along to others who may enjoy them!


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