E394 in the Enestrom index. Translated from the Latin original, "De
partitione numerorum in partes tam numero quam specie datas" (1768).
Euler finds a lot of recurrence formulas for the number of partitions of \$N\$
into \$n\$ parts from some set like 1 to 6 (numbers on the sides of a die). He
starts the paper talking about how many ways a number \$N\$ can be formed by
throwing \$n\$ dice. There do not seem to be any new results or ideas here that
weren't in Öbservationes analyticae variae de combinationibus", E158 and "De
partitione numerorum", E191. In this paper Euler just does a lot of special
cases. My impression is that Euler is trying to make his theory of partitions
more approachable,. Also, maybe for his own benefit he wants to say it all
again in different words, to make it clear.