Hannah’s Sweets: My Thoughts on the Solution

In June of this year there was an outcry amongst UK sixteen-year-olds in the wake of this GCSE probability problem:

Hannah

So, speaking as a mathematician (and a former college professor), here’s my take on this:

First and foremost, you can be sure of two things:

  • There is a solution, and

  • It’s simple.

Test-makers at the public-school level do not have time to plow through great, long, unwieldy answers to basic maths problems.

We *really* don't want to see this.
We *really* don’t want to see this.

You may be caught off-guard momentarily, but calm down, use what you know , and Keep It Simple.

So, what do we know? Well …

The first thing that jumps out at me is that quadratic.

It would be easy to write in an equivalent form:

n2 – n – 90 = 0

becomes

n2 – n = 90

What number, when subtracted from its square, equals 90?

Why, 10 of course!

So now, “Show n2 – n – 90 = 0″ becomes the much simpler equivalent statement


“Show n = 10.”

sweets
Sweet, eh?

Note: we are talking about a whole number of candies, so a small, simple number like 10 makes sense.


Onwards: back to What You Know.

Pulling one out of 6 orange sweets,and then one of 5 (remaining) orange sweets, from a bag of n (10, remember?) sweets looks like this:

FracsA

This resolves to    FracsB

Recall that the probability is one- third, and you get

FracsD

For n = 10 you get the true statement
FracsE

QED.

I know it’s easy to armchair-quarterback these things when you’re not sweating in a timed test– for what it’s worth, that’s my approach.

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