A clock was set right at 12 noon on 1 March, as shown. It gains 9 minutes every day. On which date will it next show the correct time?

It must gain 12 h = 720 min: $\frac{720}{9}=80$ days. From 1 March: 30 days to 31 March, 30 in April (60), and 20 more is 20 May. (19 May counts 1 March as day 1; 10 April uses only 360 min of gain.)