I downloaded the Facebook iPhone sdk 3.0 on my mac where im developing my iPhone game but the installation failed two times. Is this because I have 10.6.8 on my computer?
Here’s the message I got

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Yes, you can install the SDK on OS 10.6.8. I have just installed it myself and there were no problems.
I believe all the package does is place the SDK in your Documents folder. So, really you could just take the repo https://github.com/facebook/facebook-ios-sdk yourself and install wherever you wish.