Counterstamped coins are novelty coins. There are also considered damaged coins but they are very collectible. Many numerous kinds exist. If one searches novelty coins on the Internet you will find something to your liking I'm sure. First up is the famous Kennedy looking at Lincoln. We see a lot of these on CT. Usually in the error or what's it worth forums. It's not an error as it was done after it left the mint. Most of these will be on coins in the mid to the late sixties. Kennedy was very popular as he was young and very well liked. He was assassinated in 1963. This is the moon landing. Earth in the background, the date and the lunar vehicle are also counterstamp into the coin. Every one of these I've seen has the Year of 1969. Wonder why? Lol
