It's obvious that factoring of 36 into 3 factors and calculating their sum is a necessary first step of the solution. It makes sense to adopt some system for factoring in order to make sure that nothing is missed.
In the Factor table below the first factor starts with the minimum possible value of 1 and then gets increased by 1 whenever necessary. Similar approach is taken with the second factor for every fixed value of the first one. The third factor gets whatever is left. New factorings equivalent to ones already found are dropped along the way. The process stops when it's no longer possible to produce a new factoring.
| Factor Table | Sum Table | ||||||||||||||
| 36 | = | 1 | x | 1 | x | 36 | 1 | + | 1 | + | 36 | = | 38 | ||
| 36 | = | 1 | x | 2 | x | 18 | 1 | + | 2 | + | 18 | = | 21 | ||
| 36 | = | 1 | x | 3 | x | 12 | 1 | + | 3 | + | 12 | = | 16 | ||
| 36 | = | 1 | x | 4 | x | 9 | 1 | + | 4 | + | 9 | = | 14 | ||
| 36 | = | 1 | x | 6 | x | 6 | 1 | + | 6 | + | 6 | = | 13 | ||
| 36 | = | 2 | x | 2 | x | 9 | 2 | + | 2 | + | 9 | = | 13 | ||
| 36 | = | 2 | x | 3 | x | 6 | 2 | + | 3 | + | 6 | = | 11 | ||
| 36 | = | 3 | x | 3 | x | 4 | 3 | + | 3 | + | 4 | = | 10 | ||
Now with all possible age combinations spelled out, it makes sense to read the problem over again and to analyze the Factor and Sum tables. Do you see anything special about these tables?