IBM Ponder This #243 · July 2018

This month's challenge is based on a riddle I heard from Odelia Moshe Ostrovsky (thanks!).

Let's call a triplet of natural numbers "obscure" if one cannot uniquely deduce them from their sum and product. For example, {2,8,9} is an obscure triplet, because {3,4,12} shares the same sum (19) and the same product (144).

Find a triplet of ages {a,b,c} that is obscure and stays obscure for three more years: {a+1,b+1,c+1}, {a+2,b+2,c+2} and {a+3,b+3,c+3}.

Solution

Best opened after a real attempt

To be added.