Which of the following years will have the same calendar as 2016 ?
2044
A calendar repeats when the new year starts on the same weekday and is of the same type (leap or ordinary). 2016 is a leap year beginning on a Friday.
Odd days: an ordinary year gives 1 odd day and a leap year gives 2. From 2016 the total odd days must be a multiple of 7, and the target year must also be a leap year.
From 2016 to 2043 there are 28 years containing 7 leap years: \(21 \times 1 + 7 \times 2 = 35\) odd days, and \(35 \div 7 = 5\) remainder 0. So 2044 starts on a Friday and is a leap year.
Check: for 2028, years 2016 to 2027 give \(9 + 3 \times 2 = 15\) odd days, remainder 1, so 2028 starts on a Saturday and does not match; 2032 and 2052 also give non-zero remainders.
Hence, 2044.
Similar Questions
If the 25 th of August in a year is Thursday, the number of Mondays in that month is
If 18 th February, 2005 falls on Friday then what will be the day on 18th February, 2007?
Find the angle between the hour hand and the minute hand of a clock at 6 ∶ 10
It was Sunday on Jan. 1, 2006. What was the day of the week on Jan.1, 2010?
- A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
Find the angle between the hour hand and the minute hand of a clock at 8:20.
- The reflex angle between the hands of a clock at $10:25$ is
Important Questions from Clock and Calendar
Which day is 10 th October, 2027 ?
At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other?
Which date of June 2099 among the following is Sunday if 5 June 2022 is Sunday?
How many seconds in total are there in xweeks, xdays, xhours, xminutes and x seconds?
A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1·25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is
