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Cities can use a 36 hex grid at maximum.

It seems to me that 3 is also the maximum "range" at which one can purchase new tiles. Is this correct, or is it possible to buy land further off?

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No, you cannot buy tiles outside the city radius of 3 tiles. You can use a great Artist to culture bomb those tiles or a Great General to build a citadel next to those tiles if you need the strategic/luxury resources there, but don't want to build a city.

The city will continue to expand through culture up to a maximum radius of 5 tiles. But you need a lot of culture for that, the Angkor Wat wonder in that city is very useful for that.

You can never work tiles outside the 3 tiles radius, but you can get the resources on those tiles.

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  • +1 for the Culture bomb thing, totally forgot about that!
    – PeterK
    Commented Oct 19, 2010 at 9:46
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    First of all, as cities will eventually expand to 5 tiles, another option is to just wait :) secondly, don't you have to work tiles in order to gain the resources there? And tiles beyond a range of 3 cannot be worked.
    – Oak
    Commented Oct 19, 2010 at 9:52
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    @Oak - You just need to improve resources for them to be added to your trade network, no?
    – therefromhere
    Commented Oct 19, 2010 at 10:14
  • @therefromhere I thought you also had to work them, I'm not so sure anymore. I asked a question about it.
    – Oak
    Commented Oct 19, 2010 at 10:23
  • You can also "Culture Bomb" using a great General to build a citadel.
    – Lawton
    Commented Jun 29, 2012 at 17:56
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It is also possible to gain territory by building this a citadel with a Great General. One tactic I love is to steal some resources from the City states with that.

The downside is that it destroys the specialisation and the General on that field where you place the fortress, but I believe it's worth it, as it adds a free resource to your empire!

Also beware of the Diplomatic implications.

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  • A great general can build a citadel and claim area with that starting from gods and kings expansion, artists can't culture bomb anymore though.
    – Arperum
    Commented Sep 30, 2013 at 11:08

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