I make the answer 162. This is how it works:
Player A breaks off and snookers player B.
Player B does a foul and a Miss, giving 155 points away in the process (he can only give away 154 points before snookers are required, I know, but say he also goes in-off).
He leaves player A a free ball. Player A gets the 155 maximum with the free ball, meaning the score is 155-155.
He then wins the toss for the re-spot and pots it.
162 points in a single sequence of player A's shots, but not in a single break.
Player A breaks off and snookers player B.
Player B does a foul and a Miss, giving 155 points away in the process (he can only give away 154 points before snookers are required, I know, but say he also goes in-off).
He leaves player A a free ball. Player A gets the 155 maximum with the free ball, meaning the score is 155-155.
He then wins the toss for the re-spot and pots it.
162 points in a single sequence of player A's shots, but not in a single break.
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