Harriet tells Topaz that she is thinking of three positive integers, not necessarily all different. She tells her that the product of her three integers is $$36$$. She also tells her the sum of her three integers. However, Topaz still cannot work out what the three integers are. What is the sum of Harriet\textquotesingle s three integers? 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
The possible groups of three integers with product $$36$$ are $$(1,1,36)$$, $$(1,2,18)$$, $$(1,3,12)$$, $$(1,4,9)$$, $$(1,6,6)$$, $$(2,2,9)$$, $$(2,3,6)$$ and $$(3,3,4)$$ with sums $$38$$, $$21$$, $$16$$, $$14$$, $$13$$, $$13$$, $$11$$ and $$10$$ respectively. The only value for the sum that occurs twice is $$13$$. Hence, since Topaz does not know what the three integers chosen are, the sum of Harriet\textquotesingle s three integers is $$13$$. 