Parallelogram 9 Level 1 2 Nov 2023Pancake numbers

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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. Flipping good maths

Pi, Sandwich Theorem, Nugget Numbers... being a mathematician can make you hungry! But there’s always room for more maths.

Watch this video where Katie Steckles explains the Maths behind flipping pancakes.

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

2 marks

1.1 What is the maximum amount of flips needed to re-order a stack of 5 pancakes?

Correct Solution: 5 flips

2 marks

1.2 For three pancakes, we need three flips. Four pancakes need four flips.

Exactly how many flips are needed to reorder 20 pancakes?

  • 19
  • 20
  • 21
  • Nobody knows... yet
  • (Not answered)
2 marks

1.3 Katie showed us the new and improved formula to calculate the “upper bound” for a pancake number is 18n11, or 18×thenumberofpancakes11.

What is the upper bound for 22 pancakes?

Correct Solution: 36

Show Hint (–1 mark)
–1 mark

Try putting 22 into the formula, in place of "the number of pancakes"

Using substitution 18×2211=36

2. Another pancake puzzle

2 marks

2.1 You flip over a pancake to find some parts have been charred! What fraction of the pancake is burned?

  • 12
  • 14
  • 15
  • 110
  • (Not answered)

Each burned part has an equivalent perfectly cooked part, so half of the pancake is burned.

2 marks

2.2 You are a hungry mathematician and you are offered either one pancake with an 12cm diameter, or two pancakes with a 6cm diameter.

Assuming you would like as much pancake as possible, which option should you choose?

  • One 12cm pancake
  • Two 6cm pancakes
  • Either, its the same amount of pancake
  • (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.