### Solutions to the Blackball Pool Puzzles

The full solutions and answers to the Blackball Pool Puzzles are provided below as both text and images.

In this puzzle it is simply a case of finding the values of individual elements and totalling them for the answer.
The headless body of the player and coloured pool balls (which form a head) have separate values.
The pool table also has an individual value.
Pool Table = 1
Final Image Total = 12 points

Balls in Sequence Puzzle Solution
The solution to this depends upon working out the rules and sequences which determine the position of red, yellow, white and black balls in successive images.

Red and yellow appear no more than once each in a single numbered image.
Reds and yellows can appear only in the top left, top right, bottom right and bottom left positions.
If red and yellow happen to fall in the same position the colour becomes orange (the colour mix of red and yellow).
If any one of those positions is unoccupied by red, yellow or orange it is filled by a white ball.

For yellow balls there is a sequence of four positions.
Top left, bottom right, bottom left then top right.
That yellow sequence then begins again at the top left (image 5).

For red balls there is a sequence of three positions.
Top right, bottom left then bottom right.
That sequence is then repeated starting again at the top right (image 4).

The single black ball in each image occupies only the positions top middle, right middle, bottom middle and left middle.
The black arrow points to the position the single black ball will take up in the next numbered image.
If any of those four positions are unoccupied by a black ball they are left blank (that is remain green).

The correct answer is image 'B'

Blackball Pyramid Puzzle Solution
First of all work out the value of each layer and the total for the pyramid without including the black ball. Then add the value of the blackball and compare with the total pyramid value given in the puzzle.

Red Balls 4 X 4 = 16,
so 16 X 1 = 16 points.
Yellow Balls 3 X 3 = 9,
so 9 X 2 = 18 points.
Blue Balls 4,
so 4 x 3 = 12 points.
White Ball 4 points.

Total value without Black Ball = 50
Total including the Black Ball = 55
Given Total Value = 53
The given total is 2 points less than the calculated total (including a black ball) and 2 points is the value of a single yellow ball. So the black ball has replaced one of the yellow balls.

Blackball Poolean Logic Solution
Look at each statement in turn.
If one statement is true and the other two are false does this throw up any contradictions?

In the first statement if "1 is red" is true then it follows the second statement "2 is not red" must be false and that would mean 2 is also red, which is a contradiction.

Next, if "2 is not red" is deemed true it means ball 3 must be blue (the opposite of "3 is not blue"). It also means ball no.1 can't be red (the opposite of "1 is red").
And since "2 is not red" is seen as true it would mean none of the numbered balls are red, which is impossible.

If the last statement "3 is not blue" is true, then "2 is not red" is false and so ball no. 2 is red. That means ball 3 can be yellow leaving ball 1 to be blue ("1 is red" being false).
There are no contradictions if statement 3 is true.