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So for those who haven't heard, today a GCSE maths question went viral after numerous students complained it was too difficult to be on a test like that. For those who don't know, GCSEs are your basic qualifications before progressing onto the final 2 years of school at Advanced Level and then degree, and a minimum of a C in English and Maths is required for most jobs.

The question revolved around Hannah's sweets.

Hannah has a bag contained n sweets containing orange sweets are a number of other colours. Hannah takes one orange sweet out. She then takes another sweet (unknown colour) out. The probability of getting 2 orange sweets in 1/3rd. Prove that n^2 - n - 90 = 0


Apparently this question is stumping accountants with degrees for over 2 hours. Would any such Dakkanaut be willing to solve this seemingly impossible puzzle. I gave it a shot earlier but having finished my own Alevel, and finished GCSE two years ago with an A in maths, I really didn't care enough to finish it.

N's value below

just in case anyone needs a starting point.

Can't you just download the past paper for that exam if you really want the answer and formula?

Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

No wonder you can't solve the problem, you only included half of the information that was given in the test problem. The key part you're missing is that there are six orange sweets. Once you have that piece of information it's all just trivial algebra that anyone should be able to do very quickly. So:

Probability of two orange = (6/N) * (5/N-1) = 1/3

30 / (N^2-N) = 1/3

N^2 - N = 90

N^2 - N - 90 = 0

If the actual math problem is really a big deal on twitter, not the half-complete one you posted, then it's a sad comment on the state of math education.

just in case anyone needs a starting point.

That's not a starting point, it's a completely broken attempt that has nothing to do with the actual problem. You've assumed the thing you're trying to prove and solved for the exact value of N, when you're supposed to demonstrate that the final equation (N^2 - N - 90 = 0) follows from the initial information (how many sweets and the probability of two orange ones).

 Sinful Hero wrote:

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

The usefulness of a topic is the reason I changed my Major from History to Intelligence. The only jobs I could find for a history degree was .........teaching history.

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

A lot of these internet meme math problems are order of operations games which can be important depending on how you handle them.

That said, I use probability and statistics every day in my career.

 Ghazkuul wrote:

 Sinful Hero wrote:

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

The usefulness of a topic is the reason I changed my Major from History to Intelligence. The only jobs I could find for a history degree was .........teaching history.

You could flip burgers too. I hear a lot of History majors do that.

 Sinful Hero wrote:

 Ghazkuul wrote:

 Sinful Hero wrote:

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

The usefulness of a topic is the reason I changed my Major from History to Intelligence. The only jobs I could find for a history degree was .........teaching history.

You could flip burgers too. I hear a lot of History majors do that.

LOL your getting history majors confused with Psychology and Philosophy majors.

I have 3 buddies who have BA's in Psych or Philosophy and none of them have jobs utilizing those degrees.

If the actual math problem is really a big deal on twitter, not the half-complete one you posted, then it's a sad comment on the state of math education.

Education here in general really isn't great. Schools are focussed far more on rankings than they are on the quality of education, and teachers face increasing pressure to simply ensure passes rather than encourage pupils. Of course, As and A*s are valuable, but if the system hasn't changed since I was at High School, only a select few classes will be taught to the degree required to achieve them. For our GCSE years, we were split into sets ranging from top-set, to bottom-set, and each was taught in line with their predicted grades. Top-set classes were taught more advanced maths, because they were almost assured passes. Lower-set classes were taught the maths required for them to pass, resulting in the top one or two sets getting a better grounding in the subject, but the lower sets getting a higher chance of passing.

Since the question in... question, was noted by the exam board as being of A-A* difficulty, it's easy to imagine that a LOT of pupils would not have received the education necessary to complete it, simply because in the time it'd take to attempt to teach them more complex maths they might not understand, they could instead have been taught how to get a solid C or B. I wasn't taught a lot of what some of my friends in higher-set maths were taught, but I was taught the required maths for me to at least pass, and as long as you pass, the school couldn't give less of a damn about you.

The backlash over social media would almost certainly reflect the disbelief of those in lower sets, and given how it was a top-tier difficulty question, I'm not surprised that so many people complained. It's incredibly likely that they were never taught--at least sufficiently--how to complete the problem.

 Ghazkuul wrote:

 Sinful Hero wrote:

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

The usefulness of a topic is the reason I changed my Major from History to Intelligence. The only jobs I could find for a history degree was .........teaching history.

Isnt't that the point though?

Why else would you Major in History unless you were planning on teaching it.

I actually was seriously contemplating, pursuing PHD in History with the plan on teaching, until I saw how much money Teachers made.

So I went engineering instead. I make a lot of money, but my heart really is in History.

GG

 Ghazkuul wrote:

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

I'm a political analyst and I have to use advanced math every day, so do all the other people I know who work in analytic positions. Being able to at least understand calculus is a perquisite for success in many industries....and if you can't do basic algebra you better be good at sports, crime, or have connections.

 generalgrog wrote:

 Ghazkuul wrote:

 Sinful Hero wrote:

 Ghazkuul wrote:
Im so happy I am done with College math in all its useless forms.

so far in my professional career I have yet to encounter an instance where that math is useful.

It may not be useful to you, but college level math teachers have to use it everyday!

LOL probably the only people who use it on a regular basis, or even a remotely common basis.

The usefulness of a topic is the reason I changed my Major from History to Intelligence. The only jobs I could find for a history degree was .........teaching history.

Isnt't that the point though?

Why else would you Major in History unless you were planning on teaching it.

I actually was seriously contemplating, pursuing PHD in History with the plan on teaching, until I saw how much money Teachers made.

So I went engineering instead. I make a lot of money, but my heart really is in History.

GG

A history major for me is leading into a Masters in Library and Information Science.

I would absolutely hate to teach history, but the major helped me develop my researching and critical thinking skills, along with improving my ability to write. You'd be amazed at how many college level graduates were still stuck with the 5 paragraph essay formula.

 Peregrine wrote:

If the actual math problem is really a big deal on twitter, not the half-complete one you posted, then it's a sad comment on the state of math education.

The issue people seem to have is that the test was much more difficult than expected, and that it was game like; with that question being used as an example.

 infinite_array wrote:
You'd be amazed at how many college level graduates were still stuck with the 5 paragraph essay formula.

Writing is one of the single most underdeveloped skills in America. Being able to communicate effectively with others using the written word is a massive plus in any industry, especially now that so much is done by way of SMS and email.

You would be surprised how often you have the opportunity to use advanced math in real life if you knew how to use it. I use it frequently and can figure out things which lead to a greater understanding of my world and things around me because of it.

The question on the test was 7th grade math. That is when I took basic fractions and algebra. That question is entry level algebra, and they gave you the damn answer, so all you had to do is "show your work." That is all they wanted... Is proof of understanding of the process.

The reason people lack higher math is they never learned basic math. Memorizing math facts is not learning math. Memorizing times tables up to 10 doesn't teach you math and doesn't lay foundations for understanding. And when they try to teach math "the right way" ignorant parents cry on social media about how the tests make no sense... "Why can't they ask my genius offspring what 5*4 is and give him an A? Why does he have to show method and prove he knows what 5*4 is?"

I thank my lucky stars for my extensive math knowledge every day, and it gives me an advantage in literally every walk of life because of it.

Solving the initial problem:

There were N sweets to start.
Removing 1 Orange sweet leaves N-1 sweets in the bag.
Remaining sweets are 1/3 Orange. O/(N-1) = 1/3

3O = N-1
N = 3O + 1

N(1) = 4
N(2) = 7
N(3) = 10
...

The problem as presented is indeterminate, but we can validate for N(O-3):

10*10 - 10 = 90
100 - 10 = 90
90 - 90.

There is a piece of information missing in the way that the question is presented.

Seems no worse than many of the A-A* level questions I've seen before.

The way maths exams are structured, not every student is expected to be able to answer every question, otherwise everyone would achieve an A*.

 Deadshot wrote:


Apparently this question is stumping accountants with degrees for over 2 hours

The problem there is that most accountants are not actually that good at maths. The maths needed to be an accountant is primary school level. My wife is an accountant and I work with accountants every day.

The BBC have done a good video showing how to solve this. It is actually pretty simple once you see what you need to do. Nothing to do with Probability, in other words.

http://www.bbc.co.uk/news/education-33017299

 Kilkrazy wrote:
Nothing to do with Probability, in other words.

Well, you do have to know a bit of basic probability (the probability of two outcomes both happening is the probability of the first times the probability of the second) to set up the equation. If you don't know that you're never going to get it.

Ahh math, The thing the constantly tell you that you will need to now for the real world. Yet, once you get past algebra, if you need it, you can pay interns to do it for ya.

I read a good analogy the other days. It's like all those exercises footballers have to do, such as stepping rapidly in hoops, kick-ups and so on. None of these are ever used in a real game, but they build up the kind of skills that are needed. Maths problems are like that.

I remember an article in WD a few years back, where somebody was using trigonometry to calculate his cannon shots for his Empire army.

I decided to re-learn it myself, for when I used my own Empire force. This was back when you had to guess the range.

Never stopped my cannons from mis-firing, though

Here's another maths question:

In the UK, if you want to win the lottery jackpot, you have to pick 6 numbers from 1-49, and match all 6 that are drawn, in order to win the jackpot.

I remember seeing somebody calculate the odds,, which impressed me, and I'm sure it went like this: 49x48x47x46x45x44 = whatever

Is that the correct way for calculating the odds? I can't really remember.

 Peregrine wrote:

 Kilkrazy wrote:
Nothing to do with Probability, in other words.

Well, you do have to know a bit of basic probability (the probability of two outcomes both happening is the probability of the first times the probability of the second) to set up the equation. If you don't know that you're never going to get it.

I meant it doesn't use any probability equations.

Chance of the first sweet being orange is X/n.
Chance of the second sweet being orange, assuming the first is orange, is (X-1)/(n-1).
Multiply together to get total probability of 1/3

(X/n) x [(X-1)/(n-1)] = 1/3

We know X=6

(6/n) x [5/(n-1)] = 1/3
Multiply the brackets
30/(n²-n)=1/3
Flip it
(n²-n)/30=3
Solve
n²-n=90
n²-n-90=0

To those saying that this sort of maths has no use in life, I say that that is unfortunate view of life and a negative message to send to today's youth. A basic understanding of maths opens up great opportunities that you will have never have even considered possible.
I can understand this being an A grade question, but it isn't difficult.

@Do_I_Not_Like_That
At a guess it would be (6/49)x(5/48)x(4/47)x(3/46)x(2/45)x(1/44) = your odds.
The order of the balls being drawn doesn't matter, so the first is 6/49, whereas the last on is definitely 1/44.
So (6*5*4*3*2)/(49*48*47*46*45*44)=720/10,068,347,520=1/13,983,816
Always heard it was 1 in 14 million, so I guess this is right.

(just noticed Peregrine solved it ages ago, whoops)

Math is vastly overrated and 90% of more of what you learned at school is dead weight. You need basic algebra and having a firm knowledge of basic statistical math is useful, but other than that, unless you talk about specific jobs, you don't need much more. While on the other hand, math that actually /matters/ is widely neglected at school in favor of useless trash math. It's sad to see how many students can't solve basic % exercises yet school curriciula aim at trash math.

Math is vastly overrated and 90%

I work in industry (Power) and I can gurantee you math is not over rated. What do you think your powergrid works on? Wizards?
Try doing even a basic power calculation and you'll see why math is important

 Kilkrazy wrote:
I read a good analogy the other days. It's like all those exercises footballers have to do, such as stepping rapidly in hoops, kick-ups and so on. None of these are ever used in a real game, but they build up the kind of skills that are needed. Maths problems are like that.

This.

I like do lots of puzzles when I've got nothing else on. I'm currently addicted to cryptic crosswords. On face value there's no connection to my job (fixing aircraft). But underneath, the skills that are encouraged through lateral thinking, as well as being able to form strong logical connections, help me out on a daily basis. It also helps me to recognise the skills in my juniors that need developing.

GCSEs are back? I thought those were done away with

 Ratius wrote:

Math is vastly overrated and 90%

I work in industry (Power) and I can gurantee you math is not over rated. What do you think your powergrid works on? Wizards?
Try doing even a basic power calculation and you'll see why math is important

The key to a lock that secures a shed filled with excavating tools is of little importance to the general public. I am well aware of the importance of math in various areas as well as mine - I absolutely need math every day, even if tools usually do most of the job. I just don't make the mistake of thinking that because it's important for me, it suddenly becomes important for the general public. That'd be a lie. Most people only need basic math and that should be the focus of every education system. If a student knows how to calculate the distance between a circle and its tangent, but struggles with quickly solving simple % problems, then the system has failed. Useful math must be prioritized and unless all basic and actually useful math is safe, then throw some less useful math in and see where it sticks.