Calendars: placement practice questions

Solution

Use a known date: 1 January 2000 was a Saturday.

From 15 April 1996 to 1 January 2000 there are 1356 days; 1356 ÷ 7 leaves 5, so move 5 days back from Saturday.

So the day is Monday.

Solution

312 ÷ 7 leaves remainder 4.

Saturday + 4 days = Wednesday.

Solution

Days from 1 January to 1 August = 212.

212 ÷ 7 leaves 2, so the day is Tuesday + 2 = Thursday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 27 August 1952 to 1 January 2000 there are 17293 days; 17293 ÷ 7 leaves 3, so move 3 days back from Saturday.

So the day is Wednesday.

Solution

205 ÷ 7 leaves remainder 2.

Tuesday + 2 days = Thursday.

Solution

Days from 1 January to 1 July = 181.

181 ÷ 7 leaves 6, so the day is Tuesday + 6 = Monday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 3 March 1990 to 1 January 2000 there are 3591 days; 3591 ÷ 7 leaves 0, so move 0 days back from Saturday.

So the day is Saturday.

Solution

190 ÷ 7 leaves remainder 1.

Sunday + 1 days = Monday.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2012 to 2039 the odd days add up to 35, a multiple of 7, and 2040 is a leap year like 2012.

So the calendar of 2012 repeats in 2040.

Solution

Days from 1 January to 1 July = 181.

181 ÷ 7 leaves 6, so the day is Monday + 6 = Sunday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 1 January 2000 to 19 January 2006 there are 2210 days; 2210 ÷ 7 leaves 5, so move 5 days forward from Saturday.

So the day is Thursday.

Solution

244 ÷ 7 leaves remainder 6.

Sunday + 6 days = Saturday.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2015 to 2025 the odd days add up to 14, a multiple of 7, and 2026 is an ordinary year like 2015.

So the calendar of 2015 repeats in 2026.

Solution

A year is a leap year if it is divisible by 4, but century years must be divisible by 400.

Only 2016 satisfies this.

Solution

Days from 1 January to 1 December = 334.

334 ÷ 7 leaves 5, so the day is Wednesday + 5 = Monday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 1 January 2000 to 4 June 2000 there are 155 days; 155 ÷ 7 leaves 1, so move 1 day forward from Saturday.

So the day is Sunday.

Solution

330 ÷ 7 leaves remainder 1.

Tuesday + 1 days = Wednesday.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2023 to 2033 the odd days add up to 14, a multiple of 7, and 2034 is an ordinary year like 2023.

So the calendar of 2023 repeats in 2034.

Solution

Days from 1 January to 1 March = 59.

59 ÷ 7 leaves 3, so the day is Saturday + 3 = Tuesday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 16 January 1963 to 1 January 2000 there are 13499 days; 13499 ÷ 7 leaves 3, so move 3 days back from Saturday.

So the day is Wednesday.

Solution

182 ÷ 7 leaves remainder 0.

Wednesday + 0 days = Wednesday.

Solution

Days from 1 January to 1 June = 151.

151 ÷ 7 leaves 4, so the day is Monday + 4 = Friday.

Solution

Use a known date: 1 January 2000 was a Saturday.

From 10 June 1976 to 1 January 2000 there are 8605 days; 8605 ÷ 7 leaves 2, so move 2 days back from Saturday.

So the day is Thursday.

Solution

329 ÷ 7 leaves remainder 0.

Monday + 0 days = Monday.

Solution

Days from 1 January to 1 April = 90.

90 ÷ 7 leaves 6, so the day is Thursday + 6 = Wednesday.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 1996 to 2023 the odd days add up to 35, a multiple of 7, and 2024 is a leap year like 1996.

So the calendar of 1996 repeats in 2024.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2002 to 2012 the odd days add up to 14, a multiple of 7, and 2013 is an ordinary year like 2002.

So the calendar of 2002 repeats in 2013.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2008 to 2035 the odd days add up to 35, a multiple of 7, and 2036 is a leap year like 2008.

So the calendar of 2008 repeats in 2036.

Solution

A calendar repeats when the year starts on the same day and is of the same type (leap or not).

Each ordinary year adds 1 odd day and each leap year adds 2. From 2016 to 2043 the odd days add up to 35, a multiple of 7, and 2044 is a leap year like 2016.

So the calendar of 2016 repeats in 2044.

Solution

Days from 1 January to 1 November = 305 (leap year).

305 ÷ 7 leaves 4, so the day is Tuesday + 4 = Saturday.