I add up all even numbers between $$1$$ and $$101$$. Then from my total I subtract all odd numbers between $$0$$ and $$100$$.  What is the result? 
Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers
Let the required result be $$S$$. Then  $$S= \left( {2+4+6+\cdots +100} \right)- \left( {1+3+5+\cdots +99} \right)~ $$  $$\textasciitilde\textasciitilde= \left( {2-1} \right) + \left( {4-3} \right) + \left( {6-5} \right) +\cdots +\left( {100-99} \right) $$  $$\textasciitilde\textasciitilde=50\times 1=50$$. 