Sunday Times Teaser 2989 – Pot Luck
by Andrew Skidmore
Published January 5 2020 (link)
Liam had a bag of snooker balls containing 6 colours (not red) and up to 15 red balls. He drew out balls at random, the first being a red. Without replacing this he drew another ball; it was a colour. He replaced this and drew another ball. This was a red (not replaced), and he was able to follow this by drawing another colour. The probability of achieving a red/colour/red/colour sequence was one in a certain whole number.
After replacing all the balls, Liam was able to “pot” all the balls. This involved “potting” (ie, drawing) red/colour/red/colour…red/colour (always replacing the colours but not the reds), then “potting” the six colours (not replaced) in their correct sequence. Strangely, the probability of doing this was also one in a whole number.
What are the two whole numbers?