5

[1800GAMBLER]

.. number 5 because a troll who couldn't solve them got in the way.

Dijkstra’s ball game works as follows. Initially, a bag contains 2004 black balls and
2004 white balls. At every turn, two balls are removed from the bag, and either
a white ball or a black ball is put into the bag, so that the total number of balls
decreases by one. The rules are as follows:
• If the two balls removed have different colours, then a white ball is returned
to the bag.
• If the two balls have the same colour, then a black ball is put into the bag.
The game continues until only one ball remains. What colour is it?

[tpir90036]

Answer in white:
<font color="white">
It's black. the only two possibilities for the last 3 balls remaining is BBB or WWB because there will never be an odd number of white balls in the bag. and in either situation no matter what you do you will be left with a black ball.

</font>