Parallelogram 6 Level 1 12 Oct 2023Face time

This is a preview of Parallel. You have to login or create an account, to be able to answer questions and submit answers.

Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. 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. When do clock hands overlap?

It's always a good time to think about clocks! Both analogue and digital clocks are fascinating in their own ways.

Watch this video where mathematical treasure, Cliff Stoll, asks a question to get the cogs turning.

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

2 marks

1.1. How many times do the hands of a clock cross in 12 hours?

Correct Solution: 11

2 marks

1.2. The time between each crossing is 1hr 5mins and 27 seconds (to the nearest second).

What time is the last hand crossing of the day?

  • 10.55pm and 33 seconds
  • 11.05pm and 27 seconds
  • 10.54pm and 33 seconds
  • 10.54pm and 83 seconds
  • (Not answered)
2 marks

1.3. This addition square has something unusual about it.

What number should be in the missing square?

Correct Solution: 10

Some of the squares give unexpected results, e.g. 11 + 3 is normally 14 but here we have 2.

8 + 8 usually gives 16 but instead we have 4.

After 12 the numbers start to “go round again”, just like on a 24 hour clock.

This is called modular arithmetic, and in this case in particular modulo 12.

11 + 11 = 22, but modulo 12 would give 10, just as 22.00 is 10 o’clock.

2. A glitch in time

2 marks

2.1. Leap years occur in two cases:

  • When the year is divisible by 4, but not divisible 100;
  • When the year is divisible by 400.

Which of these years was not a leap year?

  • 2000
  • 1832
  • 2200
  • 1992
  • (Not answered)
2 marks

2.2. If someone was born on the 29th February 2020, and celebrated their birthday exactly 365 days later - which date would their first birthday land on?

  • 28th February 2021
  • 29th February 2021
  • 1st March 2021
  • 2nd March 2021
  • (Not answered)

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... if not, then maybe next week.
  • 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.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, 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.

Cheerio, Simon and Ayliean.