A snooker player is setting up the table before a game, and when he starts there are no balls on the table. As he takes the balls out of the six pockets, he notices something odd - the total points value of the balls in each pocket is one higher than the total points value in the previous pocket.
When he's put all the balls in position he notices that there is one missing. he then finds this ball on the floor.
What colour is this ball?
There are 15 Reds on a snooker table, each worth one point, plus the Yellow (2), Green (3), Brown (4), Blue (5), Pink (6) and Black (7), giving a total of 42 points.
The value of the balls in the second pocket is one higher than the first. The value of the balls in the third pocket is two higher than the first. And so on until the value of the balls in the sixth pocket is five higher than the first.
$$ 1 + 2 + 3 + 4 + 5 = 15 $$
So the value of the balls in the six pockets is
$$ 6x + 15 $$
where x is the value of the balls in the first pocket.
with successive values of x from zero this equates to 15, 21, 27, 33, 39 and 45. As 45 is higher than the total value of balls available (42) it must be 39. This leaves three points missing, and thus the missing ball is green.
The total points in each successive pocket is 4, 5, 6, 7, 8 and 9.