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We find out the number of different partitions of an n-kilogram stone intothe minimum number of parts so that all integral weights from 1 to n kilogramscan be weighed in one weighing using the parts of any of the partitions on atwo-pan balance. In comparison to the traditional partitions, these partitionshave advantage where there is a constraint on total weight of a set and thenumber of parts in the partition. They may have uses in determining the optimalsize and number of weights and denominations of notes and coins.

Number of Partitions of an n-kilogram Stone into Minimum Number of Weights to Weigh All Integral Weights from 1 to n kg(s) on a Two-pan Balance