Creating 6-20 to 6-23

pages/6-20-pi.md

@@ -0,0 +1,127 @@
+# Pi = 3.2?
+
+<div class="dictionary">
+
+__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.
+
+</div>
+
+*	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. How big is a slice of Pi?
+
+We all love pi, but it has a lot of digits!  
+
+Wouldn’t life be simpler if we just rounded it a little? Made it a bit more bite size?  
+
+Watch this video about the narrowly averted disaster, when pi almost officially became 3.2.  
+
+Luckily there was a mathematician passing by!
+
+@[youtube](bFNjA9LOPsg?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
+
+::: problem id=1_1 marks=1
+__1.1__ Which state almost mistakenly legislated that pi was in fact equal to 3.2?
+
+* [ ] Alaska
+* [x] Indiana
+* [ ] Washington
+* [ ] New York
+{.col-5}
+:::
+
+::: problem id=1_2 marks=1
+__1.2__ Which classical problem was Edward Goodwin attempting to solve?
+
+* [x] Squaring the Circle
+* [ ] Proof of the RiemannReimann Hypothesis
+* [ ] The Mutilated Chess Board Problem
+* [ ] The Seven Bridges of Konnigsberg
+:::
+
+::: problem id=1_3 marks=2
+__1.3__ Which of these numbers, when rounded to 1 decimal place, would give 3.2?
+
+* [ ] 3.94
+* [ ] 3.14999
+* [ ] 3.141
+* [x] 3.15
+{.col-5}
+:::
+
+::: problem id=1_4 marks=2
+__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?  
+
+What would it’s edge length be?  
+
+![](/resources/6-20-pi/1_4-right-angle.png){image align="center"}
+
+<input type="number" solution="6"/> cm
+:::
+
+
+## 2. Triangle tangle puzzle
+<!--- 2015 () --->
+
+::: problem id=2_1 marks=3
+__2.1__ Six identical right-angled triangles fit inside a rectangle as shown in the diagram.  
+
+The rectangle measures 24cm by 29cm.  
+
+What is the total shaded area in cm<sup>2</sup>?
+
+![](/resources/6-20-pi/2-triangle-puzzle.png){image align="center"}
+
+[x] 180 cm<sup>2</sup>
+[ ] 348 cm<sup>2</sup>
+[ ] 30 cm<sup>2</sup>
+[ ] 72 cm<sup>2</sup>
+{.col-4}
+
+^^^ hint id=2_1_1 marks=1
+It looks like the rectangle has the same height as two of the triangles.  
+
+Can you find the height of the triangles by splitting up the shorter length of 24?  
+
+![](/resources/6-20-pi/2-triangle-puzzle-hint1.png){image align="center"}
+^^^
+
+^^^ hint id=2_1_2 marks=1
+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.   
+
+Can we use this to find the shorter side of the triangle?  
+
+![](/resources/6-20-pi/2-triangle-puzzle-hint2.png){image align="center"}
+^^^
+
+^^^ hint id=2_1_3 marks=1
+Now knowing that the area of a triangle can be calculated by using 1/2 × base × height.  
+
+Find the total area for __all__ 6 triangles.
+^^^
+
+---
+
+`6 × (0.5 × 12 × 5) = 180`cm<sup>2</sup>
+:::
+
+
+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.

pages/6-21-perfect-number.md

@@ -0,0 +1,94 @@
+# A Perfect Number
+
+<div class="dictionary">
+
+__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.
+
+</div>
+
+*	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. 8128 and Perfect Numbers
+
+Yes, all numbers are wonderful - but how many of them are perfect?  
+
+So far, only 47.  
+
+Watch this video explaining some quirks of the rare and elusive perfect number.  
+
+@[youtube](ZfKTD5lvToE?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
+
+::: problem id=1_1 marks=1
+__1.1__ What makes a number perfect?
+
+* [ ] All of its digits are even
+* [ ] It is even and prime
+* [x] If you add up the proper divisors you get the number itself
+* [ ] All numbers are perfect!
+:::
+
+::: problem id=1_2 marks=1
+__1.2__ How many odd perfect numbers are there?
+
+* [ ] Infinitely many
+* [ ] Only one
+* [ ] None
+* [x] We don’t know yet
+
+---
+
+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!
+:::
+
+:::
+__1.3__ What is the smallest number with exactly five divisors (including the number itself)?  
+
+* [ ] 5
+* [ ] 12
+* [x] 16
+* [ ] 36
+{.col-5}
+:::
+
+::: problem=1_4 marks=2
+__1.4__ Four only has three factors: 1, 2, and 4.  
+
+Which other numbers have an odd amount of factors?
+
+* [ ] All even numbers
+* [x] All square numbers
+* [ ] All powers of two
+* [ ] None, 4 is the only example of a number with an odd amount of factors
+:::
+
+
+## 2. What number am I thinking of?
+<!--- 2018 () --->
+
+::: problem=2_1 marks=2
+__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.  
+
+What was the number?
+
+<input type="number" solution="25"/>
+:::
+
+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.

pages/6-22-rock-paper-scissors.md

@@ -0,0 +1,103 @@
+# How to win at Rock, Paper, Scissors
+
+<div class="dictionary">
+
+__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.
+
+</div>
+
+*	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__.
+
+
+## Who needs luck when you have maths?
+
+Being a mathematician gives you superpowers, like having a slight advantage at Rock, Paper, Scissors (RPS).  
+
+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.  
+
+We trust you to use this power wisely.
+
+@[youtube](rudzYPHuewc?rel=0) _(If you have problems watching the video, right click to open it in a new window)_
+
+::: problem id=1_1 marks=1
+__1.1__ If you have just lost a game of RPS, what is the best strategy to win the next game?
+
+* [ ] Play the same move again
+* [ ] Play the move they just played
+* [x] Play the move which didn’t come up in the last round
+* [ ] Choose rock. Rock always wins.
+:::
+
+::: problem id=1_2 marks=1
+__1.2__ If you have just won a game, what is the best strategy to win the next game?
+
+* [ ] Play the same move again
+* [x] Play the move they just played
+* [ ] Play the move which would have beaten your last move
+* [ ] Quit while you’re ahead!
+:::
+
+::: problem id=1_3 marks=2
+__1.3__ When played randomly, what is the probability that a round will end in a draw?
+
+* [ ] `1/2` 
+* [x] `1/3` 
+* [ ] `2/3`
+* [ ] `1/9`
+{.col-5}
+
+---
+
+3 out of the 9 possible games will end in a draw - so the probability of a draw is `1/3` when simplified.
+
+![](/resources/6-22-rock-paper-scissors/1_3-rps-table.png){image align="center"}
+:::
+
+
+## 2. Nice dice
+
+::: problem id=2_1 marks=2
+__2.1__ An unusual die has its six faces labelled 1, 2, 3, 5, 7, 9.  
+
+If two such dice are rolled, and the numbers rolled added together, then how many different sums are possible?
+
+* [ ] 6
+* [ ] 12
+* [ ] 36
+* [x] 14
+{.col-5}
+:::
+
+::: problem id=2_2 marks=2
+__2.2__ What is the most likely result when rolling and adding two of these dice?
+
+* [ ] All possibilities are equally likely
+* [ ] 8
+* [ ] 9
+* [x] 10
+{.col-5}
+
+---
+
+![](/resources/6-22-rock-paper-scissors/1-22-dice.png){image align="center"}
+:::
+
+
+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.