How many of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ can be written as a sum of exactly two of the other numbers? 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders
I wrote $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ on my page. Adding $$1$$ to $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, and $$8$$ results in $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$. We cannot get a sum of $$1$$ or $$2$$. 