permutations – Combinatorics and pigeon hole principle

How many subsets of {1,2,3….10} , each containing at least 3 and atmost 5 elements must be selected in order to ensure that the selection contains subset A , B , C such that sum of elements of A = B = C .35 sums are possible from minimum sum 6 to maximum 35 . So by Pigeon Hole Principle, minimum 71 sets must be chosen to ensure sum as equal . But in the book where I found this question, the answer is 67 . Where am I wrong ?