Q Prove that among any 16 distinct digit +ve integer not exceeding 100 there are four distinct ones a,b,c,d such that a+b=c+d

SIR some body has given this hint to me but i am not able to explain the thing that how to prove that all the four integers are distinct

hint given

Rearrange a+b=c+d, it is equivalent to finding two sets of differences |a'-b'|=|c'-d'| for distinct a',b',c',d' in our 16. Now how big can the set be, when ?