Parallelogram 48 • Level 1 • 31 Jul 2025The most feared day

Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.

Tackle each Parallelogram in one go. Don’t get distracted.
Finish by midnight on Sunday if your whole class is doing parallelograms.
Your score & answer sheet will appear immediately after you hit SUBMIT.
Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1.

Millions of people around the world get a bit worried every time Friday 13th comes around, due to long-held superstitions.

Watch this video to see why, mathematically speaking, there’s no getting away from this date (the good news is there’s nothing to fear about this date):

(If you have problems watching the video, right click to open it in a new window)

1 mark

1.1 In any given year, what is the least number of times that Friday 13th is guaranteed to occur?

0
1
3
12
(Not answered)

As the video explains, every day of the week accompanies the 13th at least once each year.

1 mark

1.2 If Friday 13th lands in January in a non-leap year, when is the next time Friday 13th occurs that year?

February
June
October
Never
(Not answered)

For the 13th of each month, we first calculate how many days into the year we are.

Then we divide by 7 and look at the remainder.

Each remainder corresponds to a different day of the week.

October has the same remainder as January (a remainder of 6), so these two months have the same day on the 13th.

2 marks

1.3 Which of these is true for a leap year?

Friday 13th never occurs
Friday 13th always occurs in February
Friday 13th always occurs but never in February
Friday 13th always occurs and it may occur in different months
(Not answered)

2 marks

1.4 If today is Friday 13th, then what day is it exactly a year from now, assuming that neither this year or next year is a leap year?

Thursday
Friday
Saturday
Sunday
(Not answered)

Show Hint (–1 mark)

1 mark

There are 365 days in a (non-leap) year and, when you divide this by 7, the remainder is 1.

So in a year’s time, the same date will have moved on by a single day, which means it will be Saturday.

2. Bedtime books and clock puzzles

2 marks

2.1 I start a book, read three-quarters of it at bedtime, and read 22 more pages at breakfast.

Now I have 35 pages left.

How many pages are there in the book?

57
76
114
140
228
(Not answered)

Show Hint (–1 mark)

1 mark

Before breakfast, I had 57 pages left (22 + 35) and one-quarter of the book still to go.

Therefore, a quarter of the book has 57 pages and the whole book has 4 × 57 = 228 pages.

2 marks

2.2 What is the time when it is 2018 minutes before midday on Wednesday?

21:38 on Thursday
02:22 on Tuesday
14:52 on Tuesday
11:30 on Wednesday
20:18 on Monday
(Not answered)

Show Hint (–1 mark)

1 mark

2018 minutes is 33 hours and 38 minutes.

We know that 1800 minutes is 180060=30 hours, 180 minutes is 3 hours, so that 2018 minutes is 33 hours with another 38 minutes remaining.

So 2018 minutes is equivalent to 1 day, 9 hours and 38 minutes.

Counting backwards from Wednesday midday gets to Tuesday at 02:22.

Before you hit the SUBMIT button, here are some quick reminders:

You will receive your score immediately, and collect your reward points.
You might earn a new badge...
Make sure you go through the solution sheet – it is massively important.
A score of less than 50% is ok – it means you can learn lots from your mistakes.
If you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.
This was our last Parallelogram of the year, but be sure to come back in September for more puzzles and problems.

Cheerio, Simon.