My country count is currently at 734. And I consider myself as nowhere near owning "one coin from every country".
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I have seen someone post 333 is that possible, when I google # of country's I got 257.
That would be the number of countries that currently exist. The vast majority of "countries that have issued coins" no longer exist. The Roman Empire, for example, no longer exists. Prior to the Romans, every single Greek city-state considered itself a separate country and (if it could afford them) issued its own coins. There were thousands of them; I only own a couple dozen. In more modern times, the territory we now call "Germany" was, prior to 1871, divided up into hundreds of little tiny independent principalities, duchies and kingdoms, most of which issued their own coins. Several times in the past 2500 years, India has fragmented into dozens of warring coin-issuing states, only to be conquered and reunified again into a different empire.
If you throw in things like "unofficial" countries, provincial / civil war coinages and government changes, the number of possible coin-issuing countries can easily escalate into the tens of thousands.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis