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Creating 6-20 to 6-23
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‎pages/6-20-pi.md

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# Pi = 3.2?
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<div class="dictionary">
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__Noun__: Parallelogram
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__Pronunciation__: /ˌparəˈlɛləɡram/
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1. a portmanteau word combining parallel and telegram. A message sent each
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week by the Parallel Project to bright young mathematicians.
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</div>
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* Tackle each Parallelogram in one go. Don’t get distracted.
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* Finish by midnight on Sunday if your whole class is doing parallelograms.
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* Your score & answer sheet will appear immediately after you hit SUBMIT.
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* Don’t worry if you score less than 50%, because it means you will learn something new when you __check the solutions__.
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## 1. How big is a slice of Pi?
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We all love pi, but it has a lot of digits!
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Wouldn’t life be simpler if we just rounded it a little? Made it a bit more bite size?
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Watch this video about the narrowly averted disaster, when pi almost officially became 3.2.
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Luckily there was a mathematician passing by!
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@[youtube](bFNjA9LOPsg?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
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::: problem id=1_1 marks=1
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__1.1__ Which state almost mistakenly legislated that pi was in fact equal to 3.2?
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* [ ] Alaska
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* [x] Indiana
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* [ ] Washington
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* [ ] New York
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{.col-5}
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:::
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::: problem id=1_2 marks=1
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__1.2__ Which classical problem was Edward Goodwin attempting to solve?
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* [x] Squaring the Circle
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* [ ] Proof of the RiemannReimann Hypothesis
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* [ ] The Mutilated Chess Board Problem
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* [ ] The Seven Bridges of Konnigsberg
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:::
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::: problem id=1_3 marks=2
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__1.3__ Which of these numbers, when rounded to 1 decimal place, would give 3.2?
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* [ ] 3.94
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* [ ] 3.14999
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* [ ] 3.141
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* [x] 3.15
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{.col-5}
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:::
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::: problem id=1_4 marks=2
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__1.4__ It may not be possible to construct a square with the same area as a circle, but can you find a square with the same area as this triangle?
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What would it’s edge length be?
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![](/resources/6-20-pi/1_4-right-angle.png){image align="center"}
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<input type="number" solution="6"/> cm
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:::
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## 2. Triangle tangle puzzle
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<!--- 2015 () --->
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::: problem id=2_1 marks=3
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__2.1__ Six identical right-angled triangles fit inside a rectangle as shown in the diagram.
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The rectangle measures 24cm by 29cm.
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What is the total shaded area in cm<sup>2</sup>?
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![](/resources/6-20-pi/2-triangle-puzzle.png){image align="center"}
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[x] 180 cm<sup>2</sup>
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[ ] 348 cm<sup>2</sup>
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[ ] 30 cm<sup>2</sup>
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[ ] 72 cm<sup>2</sup>
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{.col-4}
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^^^ hint id=2_1_1 marks=1
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It looks like the rectangle has the same height as two of the triangles.
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Can you find the height of the triangles by splitting up the shorter length of 24?
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![](/resources/6-20-pi/2-triangle-puzzle-hint1.png){image align="center"}
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^^^
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^^^ hint id=2_1_2 marks=1
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It looks like the longer length of the rectangle is made of two long triangle sides (which we just found) and a bit left over.
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Can we use this to find the shorter side of the triangle?
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![](/resources/6-20-pi/2-triangle-puzzle-hint2.png){image align="center"}
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^^^
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^^^ hint id=2_1_3 marks=1
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Now knowing that the area of a triangle can be calculated by using 1/2 × base × height.
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Find the total area for __all__ 6 triangles.
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^^^
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---
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`6 × (0.5 × 12 × 5) = 180`cm<sup>2</sup>
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:::
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Before you hit the SUBMIT button, here are some quick reminders:
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* You will receive your score immediately, and collect your reward points.
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* You might earn a new badge... if not, then maybe next week.
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* Make sure you go through the solution sheet – it is massively important.
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* A score of less than 50% is ok – it means you can learn lots from your mistakes.
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* The next Parallelogram is next week, at 3pm on Thursday.
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* 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.
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Cheerio,
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Simon and Ayliean.

‎pages/6-21-perfect-number.md

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# A Perfect Number
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<div class="dictionary">
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__Noun__: Parallelogram
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__Pronunciation__: /ˌparəˈlɛləɡram/
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1. a portmanteau word combining parallel and telegram. A message sent each
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week by the Parallel Project to bright young mathematicians.
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</div>
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* Tackle each Parallelogram in one go. Don’t get distracted.
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* Finish by midnight on Sunday if your whole class is doing parallelograms.
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* Your score & answer sheet will appear immediately after you hit SUBMIT.
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* Don’t worry if you score less than 50%, because it means you will learn something new when you __check the solutions__.
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## 1. 8128 and Perfect Numbers
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Yes, all numbers are wonderful - but how many of them are perfect?
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So far, only 47.
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Watch this video explaining some quirks of the rare and elusive perfect number.
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@[youtube](ZfKTD5lvToE?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
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::: problem id=1_1 marks=1
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__1.1__ What makes a number perfect?
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* [ ] All of its digits are even
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* [ ] It is even and prime
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* [x] If you add up the proper divisors you get the number itself
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* [ ] All numbers are perfect!
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:::
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::: problem id=1_2 marks=1
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__1.2__ How many odd perfect numbers are there?
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* [ ] Infinitely many
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* [ ] Only one
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* [ ] None
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* [x] We don’t know yet
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---
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Although all of the 47 perfect numbers we have found so far are even, we don’t yet know if there are any odd ones - or even how many perfect numbers there are!
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:::
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:::
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__1.3__ What is the smallest number with exactly five divisors (including the number itself)?
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* [ ] 5
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* [ ] 12
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* [x] 16
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* [ ] 36
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{.col-5}
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:::
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::: problem=1_4 marks=2
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__1.4__ Four only has three factors: 1, 2, and 4.
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Which other numbers have an odd amount of factors?
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* [ ] All even numbers
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* [x] All square numbers
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* [ ] All powers of two
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* [ ] None, 4 is the only example of a number with an odd amount of factors
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:::
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## 2. What number am I thinking of?
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<!--- 2018 () --->
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::: problem=2_1 marks=2
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__2.1__ Ayliean thinks of a number, divides it by 5, adds 20 to it and ends up with the number she first thought of.
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What was the number?
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<input type="number" solution="25"/>
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:::
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Before you hit the SUBMIT button, here are some quick reminders:
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* You will receive your score immediately, and collect your reward points.
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* You might earn a new badge... if not, then maybe next week.
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* Make sure you go through the solution sheet – it is massively important.
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* A score of less than 50% is ok – it means you can learn lots from your mistakes.
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* The next Parallelogram is next week, at 3pm on Thursday.
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* 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.
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Cheerio,
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Simon and Ayliean.

‎pages/6-22-rock-paper-scissors.md

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# How to win at Rock, Paper, Scissors
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<div class="dictionary">
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__Noun__: Parallelogram
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__Pronunciation__: /ˌparəˈlɛləɡram/
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1. a portmanteau word combining parallel and telegram. A message sent each
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week by the Parallel Project to bright young mathematicians.
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</div>
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* Tackle each Parallelogram in one go. Don’t get distracted.
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* Finish by midnight on Sunday if your whole class is doing parallelograms.
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* Your score & answer sheet will appear immediately after you hit SUBMIT.
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* Don’t worry if you score less than 50%, because it means you will learn something new when you __check the solutions__.
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## Who needs luck when you have maths?
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Being a mathematician gives you superpowers, like having a slight advantage at Rock, Paper, Scissors (RPS).
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Watch this video where Dr. Hannah Fry uses a mix of human psychology and probability to give you the competitive edge at this game of chance.
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We trust you to use this power wisely.
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@[youtube](rudzYPHuewc?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
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::: problem id=1_1 marks=1
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__1.1__ If you have just lost a game of RPS, what is the best strategy to win the next game?
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* [ ] Play the same move again
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* [ ] Play the move they just played
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* [x] Play the move which didn’t come up in the last round
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* [ ] Choose rock. Rock always wins.
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:::
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::: problem id=1_2 marks=1
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__1.2__ If you have just won a game, what is the best strategy to win the next game?
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* [ ] Play the same move again
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* [x] Play the move they just played
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* [ ] Play the move which would have beaten your last move
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* [ ] Quit while you’re ahead!
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:::
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::: problem id=1_3 marks=2
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__1.3__ When played randomly, what is the probability that a round will end in a draw?
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* [ ] `1/2`
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* [x] `1/3`
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* [ ] `2/3`
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* [ ] `1/9`
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{.col-5}
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---
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3 out of the 9 possible games will end in a draw - so the probability of a draw is `1/3` when simplified.
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![](/resources/6-22-rock-paper-scissors/1_3-rps-table.png){image align="center"}
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:::
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## 2. Nice dice
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::: problem id=2_1 marks=2
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__2.1__ An unusual die has its six faces labelled 1, 2, 3, 5, 7, 9.
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If two such dice are rolled, and the numbers rolled added together, then how many different sums are possible?
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* [ ] 6
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* [ ] 12
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* [ ] 36
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* [x] 14
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{.col-5}
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:::
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::: problem id=2_2 marks=2
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__2.2__ What is the most likely result when rolling and adding two of these dice?
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* [ ] All possibilities are equally likely
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* [ ] 8
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* [ ] 9
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* [x] 10
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{.col-5}
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---
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![](/resources/6-22-rock-paper-scissors/1-22-dice.png){image align="center"}
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:::
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Before you hit the SUBMIT button, here are some quick reminders:
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* You will receive your score immediately, and collect your reward points.
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* You might earn a new badge... if not, then maybe next week.
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* Make sure you go through the solution sheet – it is massively important.
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* A score of less than 50% is ok – it means you can learn lots from your mistakes.
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* The next Parallelogram is next week, at 3pm on Thursday.
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* 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.
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Cheerio,
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Simon and Ayliean.

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