Clocks & Calendars
0/10 problems solved
Formulas & 30-Second Shortcut Tricks
Formulas
- Angle between hands at H:M = |30H − 5.5M|
- Hands coincide every 65 5/11 minutes; 22 times in a day
- Odd days: normal year = 1, leap year = 2
- Leap year: divisible by 4, centuries only if divisible by 400
Shortcuts
- If angle > 180°, report 360° − angle for the smaller angle.
- Same date next year shifts by 1 weekday (2 if Feb 29 lies in between).
Practice problems
What is the smaller angle between the hour and minute hands at 4:20?
If 15 March of a year is a Saturday, what day will 15 March be next year, given that the next year is not a leap year?
What is the smaller angle between the hour and minute hands at 4:30?
If 15 March of a year is a Tuesday, what day will 15 March be next year, given that the next year is a leap year (Feb 29 falls in between)?
What is the smaller angle between the hour and minute hands at 11:45?
If 15 March of a year is a Tuesday, what day will 15 March be next year, given that the next year is not a leap year?
What is the smaller angle between the hour and minute hands at 1:30?
If 15 March of a year is a Wednesday, what day will 15 March be next year, given that the next year is a leap year (Feb 29 falls in between)?
What is the smaller angle between the hour and minute hands at 8:45?
If 15 March of a year is a Thursday, what day will 15 March be next year, given that the next year is a leap year (Feb 29 falls in between)?
Clocks & Calendars Speed Test
1 minute per question. Use the palette to jump around; you'll see time spent on every question at the end.