How many paths can you draw on a 3x3 grid of dots without overlapping lines?

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SUMMARY

The discussion focuses on determining the number of unique paths that can be drawn on a 3x3 grid of dots, where each dot must be visited without overlapping lines. Participants clarified that paths can start from any dot and include diagonal connections, expanding the complexity of the problem. The need for clear rules regarding movement and connections was emphasized to accurately calculate the total paths. The conversation highlights the importance of defining parameters in combinatorial problems.

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moni94
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Hi. If you have a 3x3 grid of dots, how many different paths can you draw if you have to go through each dot? There can be crossing lines, but none overlaping.

e.g.:

158
924
637

Sorry for my formulation. I didn't copy this from somewhere, it's a practical problem.
 
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You need to define your rules a little more. Can we start from any dot/number? In the example you have, can you go from 9 to 8? Are only horizontal/vertical lines aloud? etc.
 
gb7nash said:
You need to define your rules a little more. Can we start from any dot/number? In the example you have, can you go from 9 to 8? Are only horizontal/vertical lines aloud? etc.

Yes, you can start from any dot and you can have diagonal lines.
 

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