Problem of the Week-2: Blue or Red?

In a large urn there are 2007 blue balls and 2008 red balls. Next to the urn is a large pile (unlimited supply) of red balls. The following procedure is repeated until there is only one ball in the urn:

Two balls are chosen at random from the urn:

i) If both are red, one is put back, the other thrown away;

ii) If both are blue, they are both thrown away and a red ball from the pile is put into the urn

iii) If they are of different colors, the blue one is put back into the urn and the red one is thrown away.

What is the color of the last ball in the urn?

Carefully justify your answer!.

Posted: 9/6/08

Submit your answers (by e-mail or hard copy) by 4 pm on 9/19/08 to Noah Aydin. Hard copy submissions must include a time stamp.

Mathematics Dept.