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A Singleton can implement interfaces, inherit from other classes and allow inheritance.
While a static class cannot inherit their instance members. So Singleton is more flexible than static classes and can maintain state.
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Go for a singleton if we:
Require a complete object-oriented solution for the application.
Need only one instance of a class at all given times and to maintain a state.
Want a lazily loaded solution for a class so that it's loaded only when required.