The total number of 1s that occur among all unordered Partitions of a Positive Integer is equal to the sum of the numbers of distinct parts of (i.e., numbers in) those Partitions.

**References**

Honsberger, R. *Mathematical Gems III.* Washington, DC: Math. Assoc. Amer, pp. 6-8, 1985.

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1999-05-26