Parallelogram 18 Level 1 4 Jan 2024Algorithmic enchantment

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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. The Magic of 6,174

6,174 seems like an unassuming, random, 4 digit number - but it has an amazing property.

Watch this video where University of Nottingham Professor Roger Bowley explains:

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

1 mark

1.1 How would you describe the algorithm to arrive at 6,174?

  • Put the digits in order highest to lowest, reverse the order, and subtract
  • Put the digits in order lowest to highest, reverse the order, and subtract
  • Put the digits in order highest to lowest, reverse the order, and add
  • (Not answered)
1 mark

1.2 What happens if you start with the number 6,174?

  • The numbers will keep getting larger, heading to infinity
  • The numbers return to 6,174
  • The numbers keep getting smaller, heading to negative infinity
  • (Not answered)
2 marks

1.3 I am about to start my day.

In which order should I cary out the following instructions?

  • D = dry youself
  • G = get out of bed
  • P = put clothes on
  • T = take a shower
  • W = wake up
  • (Not answered)

2. A mysterious set of instructions

2 marks

2.1 The “reverse and add” algorithm is famous for creating palindromic numbers (same forwards and backwards).

The steps are:

  1. Reverse the digits
  2. Add
  3. Repeat until a palindrome is achieved

How many times must you reverse and add before the number 86 becomes a palindrome?

Correct Solution: 3

Show Hint (–1 mark)
–1 mark

Start with 86 + 68, is it a palindrome?

If not, reverse the digits again and add.

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.