New Scientist Enigma 597 – Break-Uprithmetic
by Susan Denham
From New Scientist #1751, 12th January 1991
In snooker there are 15 red balls worth one point each. If a player pots a red it stays in the hole and he (or she) is allowed to try to pot one of the colours yellow, green, brown, blue, pink or black (worth 2-7 points in that order). If a colour is potted it is brought out again and the player can try for another red, and so on. This continues until all the reds have gone. Then the remaining six colours are potted in ascending order.
The total points achieved in one such run is called a “break”. For example:
red + pink + red + black + red
would be a break of 16.
Having completed the break, the player sits down and lets the other player try for a red and continue the break, and so on. At the end the winning player is the one with the higher grand total of points. A player may choose not to pot the final black if the result is already determined without it. No other rules concern today’s story.
Stephens and Hendry play a frame of snooker. Stephens starts with a break of 3, Hendry follows with a break of 4, Stephens with a break of 5, and so on, and this pattern continues to the end. As usual in quality snooker, the black was potted more times than the yellow, and the pink was potted more times that the blue.
How many times did Stephens pot the brown? And how many times did Hendry pot the brown?