Impossible coins

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Impossible Coins are coins that are impossible to collect. These occur due to programmer oversights, where coins are misplaced or simply fail to load properly. There are currently two coins considered impossible to collect, and one coin which was formerly considered impossible to collect.

Current Impossible Coins

THI Impossible Coin

Video: "A New Impossible Coin"

In Tiny Huge Island there is a row of coins from a 5 coin line spawner, one of which spawns too low below the ground. Due to a failsafe, the game unloads the coin one frame after loading it. This makes it so that instead of 5 coins being in the row, there are only 4. Though it is loaded for one frame, it cannot be collecting via cloning because cloning a coin and then collecting it requires the coin to be loaded for at least 2 frames.

Mystery Goomba

Video: "SM64 - The Mystery Goomba SOLVED"

The Mystery Goomba is a member of a Goomba Triangle in Bowser in the Sky that is (presumably accidentally) placed over the death barrier, causing it to spawn on the death barrier upon being loaded, which causes it to unload on the next frame. In addition, the radius of the Goomba triangle and the Mystery Goomba do not overlap, so it turns invisible and intangible after one frame and doesn't move. While it is possible to clone the Mystery Goomba, actually killing the Mystery Goomba and collecting its coin has been deemed impossible.

Former Impossible Coins

These are coins that were previously thought to be impossible, but were eventually collected.

The Impossible Coin

Video: "SM64 - Collecting the Impossible Coin"

This coin is a coin in THI that was thought for a long time to be impossible to collect. It is part of a row of coins, but the row is placed too low and the coin appears under the ground. The coin was initially discovered in January 2002 by GameFAQs user Josiah. Many attempted to collect the coin, and no one was able to. For this reason, it was dubbed "The Impossible Coin."
In 2014, Twitch streamer MisterMonopoli recognized pannenkoek2012 in his stream's chat, and asked him to try to collect the coin. The coin was successfully collected by pannenkoek2012 by clipping inside of the island, swimming, jumping, and kicking to the coin. He did this and uploaded a video of it on June 12th, 2014, calling it, "SM64 - Collecting the Impossible Coin".