The diagram below shows nine circles each tangent to all its neighbours. One of the circles is labelled 1. The remaining circles are to be labelled with 1, 2, 3, 3, 3, 4, 4 and 4, such that no two tangent circles have the same label. In how many different ways can this be done? This is the diagram.

Is there a formula to solve these types of questions? If yes, then please share it. It would be of great help.

Sorry if this question turned out to be very easy. I just want to know a formula to solve these questions.

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  • $\begingroup$ What do you mean with "a formula"? What kind of variables should be there? $\endgroup$
    – user
    Jun 23 at 7:16
  • $\begingroup$ This is not analytic-geometry. Ii is more similar to graph theory and combinatorics problem. I suppose there is no formula because input data is the structure of graph, which is hard to generalize. $\endgroup$ Jun 23 at 7:24
  • $\begingroup$ Ok. Thanks for the info. Just wanted to know if there was a formula or not. $\endgroup$ Jun 23 at 9:20
  • $\begingroup$ Is $2\times(2+2+2)$ a formula in the sense you are looking for? $\endgroup$
    – user
    Jun 23 at 14:49
  • $\begingroup$ Yes, Thank you so much $\endgroup$ Jun 24 at 5:03


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