Parallelogram 22 • Level 1 • 1 Feb 2024How to win at rock, paper, scissors
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.
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.
(If you have problems watching the video, right click to open it in a new window)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
- Play the move which didn’t come up in the last round
- Choose rock. Rock always wins.
- (Not answered)
1.2 If you have just won a game, what is the best strategy to win the next game?
- Play the same move again
- Play the move they just played
- Play the move which would have beaten your last move
- Quit while you’re ahead!
- (Not answered)
1.3 When played randomly, what is the probability that a round will end in a draw?
1 2 1 3 2 3 1 9 - (Not answered)
3 out of the 9 possible games will end in a draw - so the probability of a draw is
2. Nice dice
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
- 14
- (Not answered)
From all of these possible dice roll combinations we can create 14 possible totals: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, and 18.
It is not possible to roll a 13, 15, or 17.
2.2 What is the most likely result when rolling and adding two of these dice?
- 8
- 9
- 10
- All possibilities are equally likely
- (Not answered)
5 pairs five a total of 10, while all the other totals are made from only three or fewer pairs.
This makes 10 the most likely total when rolling these dice.
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.