Billy bought some candy. Each piece was one of red, yellow, or blue in colour, and each piece was either hard or soft.

1) The numbers of the combinations did not have two sequences of three consecutive numbers (such as {1, 2, 3} and {5, 6, 7}).

2) There were more yellow candies than red candies.

3) Each of the combinations had a different number of candies.

4) The numbers of the combinations did not have a sequence of four or more consecutive numbers (such as {3, 4, 5, 6}).

5) Twice as much candy was soft as was hard.

6) The total number of pieces was in the twenties.

7) There were three blue candies.

8) There was at least one candy of each of the six combinations of colour and hardness.

How many of each candy combination were 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, April 2, 2014 at noon Pacific Time.** I will post the answer shortly after.