Enigma 1059: Century break
From New Scientist #2215, 4th December 1999 [link]
At snooker a player scores 1 point for potting one of the 15 red balls, but scores better for potting any of the 6 coloured balls: 2 points for yellow, 3 for green, 4 for brown, 5 for blue, 6 for pink and 7 for black.
Davies potted his first red ball, followed by his first coloured ball, then his second red ball, and so on until he had potted all 15 red balls, each followed by a coloured ball.
After potting 15 red balls and 15 coloured balls, Davies had scored exactly 100 points; but it was interesting because in calling his score after each pot the referee had called every perfect square between 1 and 100.
Question 1: If in achieving this Davies had potted as few different colours as possible, which of the coloured balls would he have potted?
In fact Davies had brought a greater variety to the choice of coloured balls potted: for instance the 2nd, 5th, 8th, 11th and 14th coloured balls potted were all different and if I told you what they were you could deduce with certainty which ball was potted on each of his other pots.
Question 2: What (in order) were the 2nd, 5th, 8th, 11th and 14th coloured balls potted?
(In answering both questions give the colours).