其它
The numbers $$1$$, $$2$$, $$4$$, $$5$$, $$8$$, $$9$$, $$10$$, $$13$$ and $$16$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? 
Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums
$1+2+4+5+8+9+10+13+16=68$  $2$ groups: sum of each group is $34$, $34=1+16+2+5+10=4+13+8+9$  $4$ groups: sum of each group is $17$, $17=1+16=2+5+10=4+13=8+9$ 