Sally has some old buttons. They are each one of white, blue, or black. Each button has either two or four holes.

1) There is only one button colour and hole combination for which there is exactly one button.

2) For each colour, there are more four-hole buttons than there are two-hole buttons.

3) There are one, two, or three of each of the two-hole button colours.

4) The number of two-hole buttons is the same as the number of black, four-hole buttons.

5) There are exactly as many two-hole buttons of one colour as there are two-hole buttons of the other two colours combined.

6) There are two blue, four-hole buttons.

If the number of white four-hole buttons is as small as it can be (fitting the other clues), how many of each type of button are there?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, December 31, 2014 at noon Pacific Time.** I will post the answer shortly after.