We can dim ai as how many pills the person takes from day i to day i.All wo have to do is to prove that there exist am or ai-aj (1≤m≤30,1≤i<j≤30)that is equal to 11. It is easy to know that 1≤a1<a2<...<a30=48,ai≤48-1*(30-i)(as days after must have pills to take) so 12≤a1+11<a2+11<...<a19+11≤48 a1,a2...,a30,a1+11,a2+11,...,a19+11 are 49 numebers which are positive integers from 1 to 48(only 48 positive integers). It is obviously that ai≠aj,am+11≠an+11(1≤i<j≤30,1≤m<n≤19) So there must exit i,j such that ai is equal to aj+11. From day i+1 to day j,the person takes 11 pills.

Does the solution has may problem?I suppose I had done it,but probably i made some spelling or grammar mistakes.