Parallelogram 6 • Level 1 • 12 Oct 2023Face time
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. 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)1.1. How many times do the hands of a clock cross in 12 hours?
Correct Solution: 11
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)
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
2.1. 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)
2.2. 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.