Problem with elegant solution
In the figure are 11 candles and 20 paths among them. The challenge is to follow the paths by these rules:
- You have to start and end at the X .
- You can only walk along every path once.
- You get a point every time you pass a candle.
- You are allowed to pass the same candle more than once.
What is the maximum number of points you can get?
You can quite easily come to a solution by trial and error but there is a much more elegant solution.
The answer is 17.
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1 solution
The entire figure consists of candles connected to by two or five paths. You can get to the candles with two paths once and to the candles with five paths twice or else you will get stuck. There are 6 candles with five paths and five candles with two paths.
6 ∗ 2 + 5 ∗ 1 = 1 7