Question 53
The equality $2008=1111+444+222+99+77+55$ is an example of a decomposition of the number $2008$ as a sum of distinct numbers of more than one digit, whose (decimal) representation uses a single digit.
i) Find a decomposition of this type for the number $2009$.
ii) Determine, for the number $2009$, all possible decompositions of this type that use the smallest possible number of summands (the order of the summands is not taken into account).
i) Find a decomposition of this type for the number $2009$.
ii) Determine, for the number $2009$, all possible decompositions of this type that use the smallest possible number of summands (the order of the summands is not taken into account).