While Dinosaur City was one of the newest Animalian Colony, and made especially for Dinotopians, that didn't stop them from having their own version of the IAC Games.
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While the majority of them were relatively the same as they were in the other colonies, in terms of appearance the stuff that were used were made of either stone, bone, or wood, in keeping with the "Neolithic" theme of Dinosaur City.
For example, the "shotputs" and "discuses" were similar to the heavier ones used by "standard" Animalians (but with higher amounts of tungsten to be challenging to Dinotopians), but looked more like rocks that happened to be the right size and shape to use as shotputs or discuses.
The barbells, dumbbells, and other things used for the bodybuilding competition were either made to be made entirely out of stone (as in the case of the dumbbells) or were made of stone weights on long bones (as in the case of the barbells), but were otherwise functionally the same as the "modern" ones used in the rest of Animalia.
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There were also games similar to the Flier games, but were mainly toned down in terms of agility but ramped up in term of speed and endurance. While Roland and Sophie didn't take part in those, they did support JC as he took part in the Dino City Flier Games.
There was also a version of the Hunter Games which were more like sprinting races, especially since most of the "predators" were theropod Dinotopians. What was both surprising and not surprising was that Tyra was not only taking part in the Hunter Games, but also in the Track and Field events, as well as the Female Bodybuilding Competition.
While the Inaugural Match: Indominus Vs. Spinosaurus was still in Animalia at Claw Colisuem, the Dino Dome was already getting registrations for the Mesozoic Fight Club's IAC Tournament. It was generally divided into "family groups" first, then in Predator vs. Prey, before one final Championship Match.
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While Dino City was the "youngest" Animalia colony, it was undeniably part of the family, especially since it was considered a two-part colony, with Skull Island for those who were mainly aquatic Dinotopians. They weren't shut out completely, but the focus of Skull Island was on aquatic races.