Go to Text bottom

**I**t'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.

**I**n
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 |

**N**ow
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?

Use [Back] button to return to problem text