Hello lads. So I did my senior maths challenge today, and there was a question which struck me as being difficult. I even asked my maths teacher and he couldn't solve it as fast as he could. So who can run me through how you would solve the following:

abcd + abc + bcd + acd + abd + ab + bc + cd + ad + ac + bd+ a + b + c + d = 2009

Find a+b+c+d

Anyone got any idea how to do this?