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Wiktionary
tetrathlon

n. (context sports English) A contest where four successive events are participated in, usually showjumping, swimming, running and pistol shooting

Wikipedia
Tetrathlon

A tetrathlon (from the numerical prefix "tetra-" meaning four) is a team competition organized by Pony Clubs for its members. It is a variant of the modern pentathlon, without fencing. Thus it comprises the four disciplines of shooting, swimming, riding and running.

Ideally, teams consist of four members from one pony club competing against several teams from rival clubs. Competitions are usually held over two days during the summer months. It is recommended that one skill and one endurance phase is completed on each day. For example, shooting and swimming will be on the first day, riding and running on the second. The competitions are organized using many volunteers and a few paid professionals. The United States Pony Clubs is a non-profit organization and the competitions are often hosted and subsidized by sponsors of the host club, local farmers, land owners and parents.

There are three age categories, known as minimus, (8 to 11), junior (12 to 14) and senior (15 to 21). Boys and girls compete together. There is no minimum qualification standard to compete, but contests are only open to active pony club members, (in the US this means those who have attended at least three rallies that year).

At the end of the games, rosettes are awarded to the top scores in each discipline, for the highest overall scores, and for the best team performances in each of the age and sex categories.