Nrich recently updated their amazing website. I love exploring their backlog of puzzles and games — what a mother lode of resources for math club or a homeschool co-op class!
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Denise Gaskins' Let's Play Math 
There are 55 connections, since there are curved connections too.
Only 46 connections. The outer circle is a single curved line, not 10 curved lines.
For a 100 pointed rose, 5050 connection including the curves.
Agree with jay 🙂 Btw, Cool riddle ! Riddles of that kind that i see here, you can find in Da Vinci Mystery game, very interesting riddles ! https://itunes.apple.com/us/app/davinci-mystery-pro/id555498867
So basically, you guys are saying that the answer is the sum of all integers between 1 and n, inclusive, where n = the number of points. Gauss gives us the equation cnt = (n*(n-1))/2 to determine the solution. It’s worth noting that you’d still have to subtract n from this value if the circle were a polygon.
Yes, Holosim, the answer is the sum of the first n whole numbers. If you look at the lines, you will see the outermost lines form an n-sided polygon. So if you posed the puzzle within the boundary of a polygon, those lines would already be covered, which explains why you would have to subtract n from the formula.