Eddie reads at least one chapter of a $$15-$$chapter book each day. If he is asked to read a different number of chapters each day, this book can be read for at most~\uline{~~~~~~~~~~}~days. 
Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums
$$15=1+2+3+4+5$$. 