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Many are answering correclty that there are 20 different numbers. However, in order to improve upon this answer, we need to look at the Doubles and triples. With the throw of one dart, excluding the bullseyes it is possible to get 60 different numbers. Each of the 20 numbers has a double area and a triple area, so if you get a triple 19 you get 57 points. So, I would contend that there are actually 60 different numbers or points that can obtained with the throw of one dart, even though there are only 20 distint numbers designated on the board.
1 - 20, each has double and triple, then the outer bull (25) and the inner bull (50).
On a dartboard the numbers from 1 through 20 are represented. If you add 1 + 2 +3... all the way to 20, you get 210. Hope this answers your question.
Starting at 20 Working clockwise 20,1,18,4,13,6,10,15,2,17,3,19,7,16,8,11,14,9,12,5
20 unless your conting doubles and tripples of each number then there will be 60