Parallelogram 17 • Level 1 • 28 Dec 2023Coin quandaries
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.
1. The Hexacoin Puzzle
This puzzle seems impossible, but Alex Belos shows that it can be done - although it is easy to forget how!
Watch this video, remember to pause and give it a go.
(If you have problems watching the video, right click to open it in a new window)1.0 Honesty point: if you had a go at the coin puzzle, whether you completed it or not, click here for one point!
- I tried!
- (Not answered)
1.1 When the coins are moved, what rule must they follow?
- The can only be touching one other coin
- They must be touching two other coins
- They must be touching three other coins
- (Not answered)
1.2 Using the standard UK amounts of 1p, 2p, 5p and 10p, how many different ways are there to make 10p?
Correct Solution: 11
There are many logical ways to approach this. One would be to consider that there is only one solution using the 10p.
There are 10 other solutions using combinations on 1p, 2p, and 5p coins.
As shown in this venn diagram:
1.3 You have 15 one pound coins, which you divide into 4 money bags.
The coins are divided such that you can hand over any amount from £1 to £15 without opening a bag, just handing over a combination of money bags.
How are coins divided?
- £1, £3, £5, £6
- £1, £2, £4, £8
- £2, £3, £4, £6
- £1, £1, £6, £7
- (Not answered)
2. When life gives you (puzzles about) lemons
2.1 Oranges cost 26p each and lemons cost 30p each.
Gordon spent exactly £5 on a mixture of oranges and lemons.
How many oranges and lemons altogether did he buy?
- 16
- 17
- 18
- 19
- 20
- (Not answered)
£5 is a multiple of 10, the cost of a lemon is also a multiple of 10.
This means we need to buy enough oranges to make the total price of the oranges a multiple of 10.
If the cost of the oranges must be a multiple of 10, then we have bought either 10 or 20 oranges.
For a total of £5, only one of these is possible.
£5 is a multiple of 10, the cost of a lemon is also a multiple of 10.
This means we need to buy enough oranges to make the total price of the oranges a multiple of 10.
If the cost of the oranges must be a multiple of 10, then we have bought either 10 or 20 oranges.
20 oranges would cost £5.20, which is too much!
So we have 10 oranges at a cost of £2.60 and then with the remaining £2.40 we can buy 8 lemons, giving us a grand total of 18 fruits all together.
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.