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Booby Kids Nintendo
This was only released in Japan, on July 10th 1987. To the best of our knowledge it is not actually about children with large breasts.
Despite its dubious name, the word "booby" probably refers to the main's character's ability to dig holes to trap enemies like a booby trap. The game is a mix of Bomberman, Lode Runner and Heiankyo Alien, where the goal is to collect all the items in the stage while avoiding the respawning enemies. The player can also set bombs, needed to destroy obstacles in the way of some of the collectibles and can also be used to defeat enemies.
The game moves through time periods, starting in the prehistoric era with cavemen and dinosaurs and moving onto samurai era Japan and other chronologically diverse settings.