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Minimum number of partitions required for obtaining all numbers from $1$ to $n$
I took part in a coding contest organized by a club in my college for freshers, In one of the problems it was asked to find out the minimum number of partitions of a number $n$, so that all the ...
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# of partitions of $n$ into at most $r$ positive integers $=$ # of partitions of $n + r$ into exactly $r$ positive integers?
How do I see that the number of partitions of the integer $n$ into at most $r$ positive integers is equal to the number of partitions of $n + r$ into exactly $r$ positive integers?
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