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by Brian Gladman on January 4, 2020

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?

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