The NMC was founded in 1986 during the International Mathematical
Olympiad (IMO) in Warsaw. The leaders of the teams from the four
Nordic countries which at that time took part in the IMO (Denmark did
not join the IMO until later) agreed that their students needed a
competition which in difficulty would lie somewhere between the
national competitions and the International Mathematical Olympiad

(Åke H. Samuelsson, Normat **36**:27
(1988), translated from Swedish). The practical arrangement should be
kept at a minimum. Sweden volunteered to be the first host of such an
event and organised the first NMC, which was held on 30 March 1987. In
1988–1990 subsequent NMCs were hosted by Norway, Iceland and Finland,
in this order. In the beginning, the competition was called *The
Nordic Mathematics Olympiad*. The name changed to the present one
in 1991.

In 1989 a single Danish student was allowed to write the exam in a school in Sweden, and in 1990 a handful of Danish students took part in the NMC. In 1991 Denmark joined the IMO, and it was suggested that Denmark should then host the 5th NMC. But since the Danes had yet so little experience with international competitions, Sweden accepted to organise the NMC for a second time. Denmark would then be the host in 1992, and in the future, the cyclicly repeated hosting order should be the present one: Sweden, Norway, Iceland, Finland, Denmark. Since then, an NMC has taken place every spring organised by countries taking turns in this order.

For a more detailed account of the history of the NMC, see this Wikipedia article, which has also references to the available written documentation.