MathDB

n

is a given positive integer, such that it’s possible to weigh out the mass of any product weighing

1,2,3,\cdots ,n\text{g}

with a counter balance and

k

counterweights, whose weights are positive integers. (a) Find

f(n)

: the minumum value of

k

. (b) Find all possible number of

n,

such that the mass of

f(n)

counterweights is uniquely determined.

Problem Statement