#Edexcel solution explained here

I turned on Twitter to see that “Edexcel”, whatever that is, is some kind of maths problem that students were tweeting about.

15 - 1

The problem is this:

The question told pupils that Hannah had a bag containing a total of n sweets of which 6 were orange. It said the chances of Hannah picking two orange sweets one after the other was one third and then said use that to prove that n²-n-90=0.

In order to see if I still had any mathematical ability left, I tried to give the problem a go.

As it happens, the problem is easy.

The probability that the first sweet is orange is 6/n. Once that is taken out of the bag, there are n-1 sweets left, 5 of which are orange. So the probability that the second sweet is orange is 5/(n-1).

We are told that the probability that the first and the second sweet are orange is 1/3. i.e.
[6/n] * [5/(n-1)] = 1/3

Cross-multiply the two sides of the equation:

6 * 5 * 3 = n * (n-1)

which rearranges to
n^2 -n – 90 =0


What we should really be asking is why adults can’t seem to solve this problem.

Update 04-Jun-2015: So many does she have, anyway?

To work that out, we simply solve a quadratic the quadratic, which you’ll recall is:
n = [-(-1 ) + sqrt(-(-1) -4 *1 *(-90))/2
= [1 + sqrt(91)]/2 (you can ignore the negative root)
= [1+19]/2
= 10

Note that there are two roots. One of them is negative, which you can ignore, because you can’t have a negative number of sweets in a bad.

Old joke: A mathematician sees two men enter a bar. Soon after, three men leaves. He says to his friend: “when another man enters the bar, it will be exactly empty”.

Edit 25-Jun-2015: Added picture

About mcturra2000

Computer programmer living in Scotland.
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6 Responses to #Edexcel solution explained here

  1. Daniel Victor says:

    I worked out what n was in under two minutes – by trial and error.Proving the equation is far harder – you have to learn how to do that.

  2. mcturra2000 says:

    As my statistics lecturer once said to the class: I hope you all get the grades you deserve.

    Needless to say, there were groans throughout the room.

  3. mcturra2000 says:

    Please note, I am not a teacher, and haven’t studied mathematics in many years. So I do not know what it in the curriculum. Given that I therefore know nothing, I would, in Edexcel’s defence, it seems that they were trying to test examinees’ higher-order thinking skills. This is a reasonable thing to do. Examining boards have taken a lot of flak for dumbing down their tests, so perhaps people can’t complain when they ask difficult questions.

    What do the maths teachers out there think?

  4. paddy says:

    Considering your job is programmer which involves solving equation, and your blog tag line is “Investing, mathematics, programming”, this is probably the reason why you found it easy. Other of us in not such maths heavy professions struggle.
    Thanks for the solution.

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