In last week's series opener at Lord's, England were celebrating with pints of Guinness by lunch on day three, marking an innings victory in James Anderson's farewell outing, but they were made to work considerably harder in Nottingham.
A last-wicket stand of 71 between Josh Da Silva and Shamar Joseph handed the tourists a 41-run lead, frustrating the hosts as they failed to kill off an innings that sprawled to 457.
England were still 34 behind when Zak Crawley was unluckily run out by a fingertip touch at the non-striker's end and could easily have found themselves in a spot of bother. But an enterprising knock of 76 from Duckett set them on their way to a stumps score of 248 for three.
Brook took over in the evening session, showcasing some wonderfully instinctive strokeplay as he racked up an unbeaten 71 in bossing a 108-run partnership with Joe Root (37no).
Duckett, whose very participation had been in doubt due to the imminent arrival of his first child, hit 71 in 59 balls in the first session of the game and followed up with another impactful effort at the head of the innings.
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