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# Hannah's sweets solution: the GCSE question that stumped UK students

Students flooded social media this week to vent their frustration at Edexcel’s GCSE Maths paper featuring a problem involving how many sweets a girl called Hannah has.

But what actually was the problem and how hard is it to actually solve? Well, here it is – but don’t read below the images if you want to work it out yourself.

The problem

Hannah has 6 orange sweets and some yellow sweets.

Overall, she has n sweets.

The probability of her taking 2 orange sweets is 1/3.

Prove that: n^2-n-90=0

^ is “to the power of”

The number of students posting about the tricky problem caused the question to trend on Twitter and although they may not have got the marks in the bag, they certainly got their memes spot on.

Hannah’s was just one of the many supposed “real life” problems that the students were required to tackle.

Another problem required students to calculate how much a child had raised for charity and find which garden centre sold the cheapest plants.

There are 6 orange sweets and n sweets overall. So, if Hannah takes one, there is 6/n chance of getting an orange sweet. When she takes one,, there is one less orange sweet and one less overall meaning that the probability is now (6-1)/(n-1)=5/n-1.

To find the probability of getting the orange sweet both times, multiply the two fractions: 6/n* 5/n-1 =30/n^2-n.

It shows the probability of taking two orange sweets (1/3) is: 1/3=30/n^2-n.

The denominators then need to be the same, so multiply 1/3 by 30 which would then make 30/90=30/n^2-n.

Discounting the 30 on both sides of the equation makes n^2-n=90. By moving 90 onto the other side of the equation, it will equal zero.

Simple, right?

Independent News Service