8,9 |
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Ten points are marked on a circle. How many non-closed, non-self-intersecting nine-segment broken lines with vertices at these points exist?
Solution
The first point can be chosen in ten ways. Each of the following eight points can be chosen in two ways: it must be adjacent to one of the previously chosen points (otherwise, a self-intersecting broken line would result). Since the beginning and end are distinguishable in this counting, but not in the broken line, the result must be divided by 2. Therefore, there are broken lines.
## Answer
1280 broken lines.
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