How to solve the maths GCSE question about Hannah's sweets that went viral

Students took to Twitter to moan about how difficult the question was.

I agree, there is something inherently comic about the question, since you start off talking about Hannah and sweets and then - BANG - all of a sudden you get a scary-looking equation. 

But READ THE QUESTION. The question is not asking you to solve the equation. It is asking you to do some basic probability.

Let’s solve it:

If Hannah takes a sweet from the bag on her first selection, there is a 6/n chance it will be orange.

That’s because there are 6 oranges and n sweets.

If Hannah takes a sweet from the bag on her second selection, there is a 5/(n-1) chance it will be orange.

That’s because there are only 5 orange sweets left out of a total of n - 1 sweets.

The chance of getting two orange sweets in a row is the first probability MULTIPLIED BY the second one. (That’s the most important thing to learn from your lesson today, peeps!)

Which is 6/n x 5/n–1

The question tells us that the chance of Hannah getting two orange sweets is 1/3.

So: 6/n x 5/n–1 = 1/3

All we need to do now is rearrange this equation.

(6x5)/n(n-1) = 30/(n2 – n) = 1/3

Or 90/(n2 – n) = 1

So (n2 – n) = 90

Voila: n2 – n – 90 = 0

MINGWEN B. GCSE Physics tutor, GCSE Maths tutor, GCSE Chemistry tutor

11 months ago

Answered by MINGWEN, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Alex D.

Degree: Maths and Philosophy (Masters) - Bristol University

Subjects offered: Maths, Philosophy


“Now studying Maths and Philosophy at Bristol, I have a great passion for the intricate workings within Maths and the endless possibilities and ideas within Philosophy. I hope that through my tutorials I will be able to pass on some of ...”

MyTutor guarantee

£22 /hr

Nathan L.

Degree: Materials Science (Masters) - Oxford, St Edmund Hall University

Subjects offered: Maths, Physics+ 1 more


“About Me: I'm a first year Materials science undergraduate at The University of Oxford. I loved learning about science and maths at school and hope my tutorials make you feel the same.  Structure: The key concept about tutorials i...”

£18 /hr

Charles B.

Degree: Classics (Bachelors) - Durham University

Subjects offered: Maths, Latin+ 1 more

Classical Civilisation

“About me I'm a passionate classicist particularly focused on ancient military warfare  currently studying classics at Durham University. I've been studying Latin and  Ancient History since I was 9 years old, picking up Ancient Greek at ...”

About the author

£18 /hr


Degree: PhD in Materials (Doctorate) - Manchester University

Subjects offered: Maths, Physics+ 1 more


“Dr. Mingwen Bai 29 Boyton Close, London E1 4AN   07440467703     Personal profiles                                                           Objective: professional teaching or tutori...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How do you substitute a number into an algebraic expression?

​What's the difference between the mean, median and mode? Why are there so many different types of average?!

Solve the simultaneous equations, 5x + 2y = 20 , x + 4y= 13

Find the maximum or minimum value of the function: y = 6x^2 + 4x + 2

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss