Calendar Questions

Exact angle between clock hands at 1:40 — Compute the smaller angle between the hour and minute hands at 1:40 am.

Exact angle between clock hands at 10:10 — Compute the smaller angle between the hour and minute hands at 10:10 am.

Exact time of coincidence between 3 PM and 4 PM — At what time between 3 and 4 do the hour and minute hands coincide?

Exact time when hands are opposite between 3 PM and 4 PM — At what time between 3 and 4 are the hour and minute hands 180° apart?

Times when hands are at right angles between 4 PM and 5 PM — At what time(s) between 4 and 5 are the hands 90° apart?

Clock problem — between 9:00 PM and 10:00 PM, at what exact time are the minute hand and the hour hand opposite to each other (i.e., separated by 180 degrees)? Provide the answer in the form 9 : mm (with fractional minutes allowed).

Clock problem — between 9:00 PM and 10:00 PM, at what exact time do the minute hand and the hour hand coincide (overlap)? Answer in the form 9 : mm (fractional minutes allowed).

Calendar arithmetic — If 14 October 2005 was a Friday, then what day of the week was 14 October 2006?

Calendar arithmetic — If today is Monday, what day of the week will it be after 59 days?

Calendar arithmetic — If 14 October 2005 was a Friday, then what day of the week was 14 October 2009?

Calendar arithmetic — If 2 June 2012 was a Saturday, what day of the week was 7 July 2012?

Calendar arithmetic — If 1 January 2001 was a Monday, then what day of the week was 1 January 2013?

Leap-year identification — Which of the following is not a leap year under the Gregorian rules?

Leap-year identification — Which of the following is a leap year under the Gregorian rules?

Calendar arithmetic — If 1 January 2006 was a Sunday, what day of the week was 1 January 2010?

Calendar arithmetic — If today is Sunday, what day will it be after 69 days?

Calendar arithmetic — If 6 March 2005 was a Sunday, what day of the week was 6 March 2002?

Clock angle — What is the angle between the minute hand and the hour hand at exactly 11:50 AM?

Clock angle — Between 2 PM and 3 PM, at what exact time is the angle between the minute and hour hands equal to 100 degrees? Answer as 2 : mm (with fractional minutes if needed).

Clock angle — What is the angle between the minute hand and the hour hand at exactly 2:18 AM?