Tuesday 13th August 2024

Dear Lindsay

Now that I am getting on (I turn 70 today) I want to give you some of my money. I shall give you a sum each year, starting now. You can choose which of the following schemes you would like to use.

1. £100 now, £90 next year, £80 the year after, and so on.

2. £10 now, £20 next year, £30 the year after that, and so on.

3. £10 now, one and a half as much next year, one and a half as much
again the year after, and so on.

4. £1 now, £2 next year, £4 the year after, £8 the year after that, and
so on.

Of course, the scheme can only operate while I am alive. I look forward to hearing which scheme you choose, and why.

Sincerely

Aunt Lucy

This investigation comes from the 1989 Hertfordshire Information Technology Across the Curriculum (Mathematics and Data Handling) project document.

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A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is
closed. Investigations can always be extended by varying the initial
instructions or asking the question 'what if...?'. Sometimes students point out
that the instructions are ambiguous and can be interpreted in different ways.
This is fine and the students are encouraged to explain how they interpreted the
instructions in their report.

Some students may benefit from a writing frame when producing the reports
of their investigations. Teachers may suggest sections or headings such as
Introduction, Interpretation, Research, Working and Conclusion or something
similar.

The Maths Class Of 9p, The Teacher Miss Whitaker

Wednesday, November 30, 2011

"I think the second one."

Miss Hopson, Little School For Stars

Thursday, February 16, 2012

"We like the first one."

Tina, 8c

Wednesday, September 19, 2012

"The second one."

Tom And George, The Grammar School

Wednesday, November 28, 2012

"We think it is the forth one."

Tom And George, HGS

Friday, November 30, 2012

"We Think that it is the third one, because life expectancy means she will say she lives ten years and 3 gives you the most money."

5EH WHCS, Aylesbury

Tuesday, December 11, 2012

"As a class, we agree that option 4 is the best solution because after 10 years, it's the most lucrative. Assuming she lives an average life expectancy!"

Year 5 Set 1, William Harding School

Monday, December 16, 2013

"We think that option 4 is the best because over a long period of time, you would receive £32,767.

Option 1 is the least profitable if she lives longer. However, this is the best option in the first 5 years.

5EH."

Ryan, APA

Tuesday, March 4, 2014

"I like the third one because you get a high amount getting slowly more."

Tishya, Garden International School

Tuesday, April 29, 2014

"I think it is the second one."

Kyle, Oxted School

Tuesday, July 11, 2017

"I think that No.1 is the most profitable if she lives longer however if she lives shorter No.1 I the best choice."

Romain B, LIS - 3MS

Wednesday, September 6, 2017

"I think it is the fourth one. If she still lives 10 years, it is the one that brings the most money."

Leonard.s, LIS 3MK

Saturday, September 9, 2017

"I think it is the 4 one because if Aunt Lucy gets to be 84 (which is the average) I would get 16.383"

Yasmin, 3MK LIS

Sunday, September 10, 2017

"I think the option 3 is the best if she lives for 10 years."

Tracy, Nexus International School Malaysia

Wednesday, December 6, 2017

"I think it's option 4. Even though Aunt Lucy lives until 90 year old or older, the sum of option 4 is still more than all the others options."

Meriel, LIS 3AMT

Sunday, September 23, 2018

"If she lives 5 more year`s then option 1 is the best. I don´t think option 2 is a good option because it goes up so slowly. Option 3 would be good if she lives 10 more years. But I am going to go for number 4 because if she gets higher then 10 then I get loads of money!"

Cameron, Sir John Talbot's School, Shropshire

Saturday, March 23, 2019

"I don't think No.1 is a good option becaif she lives longer than 10 years, the amounts become negative, which subtracts from your money, not adds to it! No.4 grows exponentially each year (so does No.3, but No.4 grows quicker) which, in effect, is better than No.2, which only grows by only £10 each year. So, I think No.4 is the best option."

Cool Person, My Home

Friday, April 5, 2019

"I choose option 4 as it is the most profitable after 9 years. However, if Lucy dies 5 years later I would choose option 1. If Lucy dies 9 years later I would choose option 3 as the total profit is bigger than option 1 (9 years later). Option 2 is the worst becait starts at 10 dollars and it increases very slowly."

Qasim Elemam, 5 Galalieo

Monday, November 11, 2019

"Number 1 for me is the best option if she was just about to die.Number 2 if she had a 100-90 % of living becashe would be building up by ten.Number 3 if we needed money becait gets times ed by two.Number 4 if you wanted to be nice and get cheap."

5 Galileo, Parramatta Public School

Monday, November 11, 2019

"If she lives a year or 10, then option one is the most suitable and profitable. However, if she lives for 10 or more years, option two and four are the best."

Hi, Pps

Monday, November 11, 2019

"I think its option 3 as you are multiplyng the numeral by 1 and a half which gives you more than the other options ( I and 2 are equivelant )."

Lily Hughes, Claremont

Wednesday, April 29, 2020

"I’d say number 1. It secures more money and we don’t know how long the aunt will live. If she would to die, then they would stop receiving money. If she died a year later you would only make a smaller amount."

Year 7's Of 2020, OneSchool Global, Swan Hill Campus

Thursday, August 20, 2020

"We think the first one, especially because Aunt Lucy is likely to die soon. After all, it's better safe than sorry!"

Mansur, Bedfont Primary School

Friday, January 29, 2021

"I will choose the third one because you get smaller at the first but then go more higher and higher with each one."

Irina, Maryland

Tuesday, February 23, 2021

"The second one if she lives 20-30 years

the first one if she lives <=10 years."

Mathsclub1, Herts

Thursday, February 25, 2021

"We like Schemes 2 and 4 as you will probably have the most money based on the average life expectancy!"

Somaya, Franklin Elementary

Thursday, April 29, 2021

"I think the 1st one because she isn't going to to live for more thank 30 years."

Anna, Vancouver

Saturday, June 26, 2021

"I think the 1st option is the best. Choosing the second or the forth option is better if she lives for more than 10 years, but this would be a a big risk."

Shlok, Kerala

Sunday, July 25, 2021

"I choose scheme 2.lets say that aunt Lucy lives for 20 more years ,I can get about 100+ euros guaranteed .And if she lives fore 10 years, I can get about 70+euros guaranteed."

Xenia, A Student

Wednesday, October 6, 2021

"I think the 4th one because it doubles each time and if you get to 100 then 200 soon it will be a thousand."

ling Pizza, Paris

Monday, November 22, 2021

"We choose the third option, because it's both safe, (at least more than the fourth option for the first 10 years) and it won't run out(like the first option will) and its simply more than the second one."

Anon, Crofton

Tuesday, June 28, 2022

"I would put option 4, as if the life expectancy of a healthy female is about 80 years, she would live ten more years, therefore earning £863 after a bit of patience. Of course, if she lives longer you earn more, but of she lives shorter due to an infection or disease then you of course earn less."

William Knapp, Brighton College Year 6

Monday, September 12, 2022

"If the granny lived for a very short period (less than 3 years) I would go for the first one. But if the granny lived for the 30 years I would go for the third one."

Frederick,

Thursday, September 15, 2022

"Life expectancy suggests that Aunt Lucy will live about 10 more years so the most ideal for the first 10 years is either 1 or 2. It depends on weather you want the most money flowing in at first."

Maxwell, IPS Mauritius

Thursday, March 21, 2024

"Option 4 all the way. By the end of the year. You will get more than 5 million euros."