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The grey install DVDs are machine specific and will only work on the machine type they are shiped with.

Agreed.

You can sometime be lucky if you have grey restore DVDs for your exact machine type (e.g. Mac Mini (Early 2009); Mac Mini (Late 2009); etc.

However, in the OP's specific case, the G4 Minis were never shipped with Leopard, so there won't be any Restore DVDs to suit.
 
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