I have the following problem, quoted directly from Biggs, Discrete Mathematics:
A golfer has $d$ days to prepare for a tournament and must practice by playing at least one round each day. In order to avoid staleness he should not play more than $m$ rounds altogether. Show that if $r$ satisfies $1\leq r\leq 2d-m-1$, then there is a sequence of consecutive days during which he plays exactly $r$ rounds.
I'm not asking for a full solution, but rather for a hint on how to start. Any ideas?