Author Topic: Another pair of kids' logic problems (Read 8384 times)

Wowbagger · « **on:** 08 June, 2015, 05:55:16 pm »

http://www.theguardian.com/science/2015/jun/08/can-you-solve-it-are-you-smarter-than-a-hong-kong-six-year-old

I love the odd-one-out puzzle. I solved the parked car one instantly and didn't think it was that good, but I imagine it will catch a few people.

Pancho · « **Reply #1 on:** 08 June, 2015, 06:13:40 pm »

I think I've got the odd-one-out.

On the topic of hard exams - did anyone[1] find that "Hannah's sweets" gcse question anything but utterly straight forward?

[1] anyone like me and people around me (maths-y / engineery types). I'd be crap at English, or public speaking - we all have our strengths.

Wowbagger · « **Reply #2 on:** 08 June, 2015, 06:18:08 pm »

I couldn't do it at all. I didn't understand the solution when put forward either.

pcolbeck · « **Reply #3 on:** 08 June, 2015, 06:18:39 pm »

Hannah's sweets was quite easy for anyone who has done any kind of probability maths (which should include those taking a Maths GCSE).
What it demonstrated was that a lot of students had only rote learning and hadn't been taught to use maths to solve problems. I would think if the question had been phrased in a more standard way a lot more students would have got it.

Oaky · « **Reply #4 on:** 08 June, 2015, 06:19:09 pm »

I'd seen the parked car one before (through Bookface, probably). The odd one out question is very good though!

red marley · « **Reply #5 on:** 08 June, 2015, 06:20:53 pm »

The shapes/sizes/colour puzzle:

Is the answer the 'all the greenish grey ones' these are the ones that have a unique colour for those with red/green colour blindness?

As for Hannah's sweets, I thought it was a great question as it is all about applying basic probability and equation rearrangement skills rather than just learning them.

Wowbagger · « **Reply #6 on:** 08 June, 2015, 06:25:10 pm »

Quote from: pcolbeck on 08 June, 2015, 06:18:39 pm

Hannah's sweets was quite easy for anyone who has done any kind of probability maths (which should include those taking a Maths GCSE).
What it demonstrated was that a lot of students had only rote learning and hadn't been taught to use maths to solve problems. I would think if the question had been phrased in a more standard way a lot more students would have got it.

My problem with any sort of maths equations, and the rearranging of the elements on either side, is that I am very pedestrian at it. I just "don't get" it in a way that I do, for example, "get" chess problems.

pcolbeck · « **Reply #7 on:** 08 June, 2015, 07:11:03 pm »

Quote from: jo on 08 June, 2015, 06:20:53 pm

As for Hannah's sweets, I thought it was a great question as it is all about applying basic probability and equation rearrangement skills rather than just learning them.

Exactly that was the rub. If they had just been asked to work out the probability of getting two orange sweets as the first two draws out of the bag or given the messy equation that results and told to simplify it most students would have been able to do it or at least understood the question. What they actually got was an example of how maths is used in the real world (well it wouldn't be sweets but something else involving the same ideas such as insurance or calculating the MTBF of something).

pcolbeck · « **Reply #8 on:** 08 June, 2015, 08:11:11 pm »

Its easy WoW. All you need to know is that the probability of independent events (ie events that are unconnected like tossing a coin multiple times or in this case picking sweets out of a bag) is found by multiplying the probability of the individual events occurring together.

Lets start easy with tossing a coin. What's the probability of getting a head ?
Well a coin has two sides only one of which is a head so the probability (p) of flipping it and getting a head is 1/number of possible outcomes (n)

$p= \frac{1}{n}$

This is a 1/2 since a coin can only end up heads or tail ie n =2

So we know there are 6 orange sweets in the bag so whats the probability of sticking your hand in and pulling out an orange sweet ? Just like tossing a coin it's the number of picks that give us the desired outcome divided by the total number of possible outcomes. So:

$p= \frac{6}{n}$

Now we have our first orange sweet what's the probability of a pulling a second out. Well there are now only 5 orange sweets left and one less sweet total in the bag. So:

$p= \frac{5}{n-1}$

So what's the probability of pulling two orange sweets out as the first two picks ? Remember we just need to multiply them together:

$p= (\frac{6}{n})*(\frac{5}{n-1})$

This can be simplified by multiplying the two fractions:

$p=\frac{30}{n^2-n}$

Now we have been told that the probability of getting two orange sweets is 1/3 so replace p with 1/3:

$\frac{1}{3}=\frac{30}{n^2-n}$

Nearly there ! Mutiply both sides by three:

$1=\frac{90}{n^2-n}$

Mutiply both sides by n^2-n:

$n^2-n=90$

Subtract 90 from both sides:

$n^2-n-90=0$

Job done !
And its also then obvious that n =10.

Wowbagger · « **Reply #9 on:** 08 June, 2015, 08:50:29 pm »

I can follow it up to p=1/n when applying to coins.

After that, I'm flummoxed.

Wowbagger · « **Reply #10 on:** 08 June, 2015, 09:53:31 pm »

I've been giving this some thought, and once I knew that there are 10 sweets in the bag, I could follow the logic. I have never been able to cope with unknown numbers represented by letters. I have never been able to master the tricks of shuffling the sides of an equation without actually knowing what numbers the letters represented. Couldn't do it at O level (grade 6) when I had a fairly alert mind and quite a lot of practice, certainly can't do it now after a 45-year gap..

jsabine · « **Reply #11 on:** 09 June, 2015, 12:54:41 am »

Quote from: pcolbeck on 08 June, 2015, 07:11:03 pm

What they actually got was an example of how maths is used in the real world (well it wouldn't be sweets but something else involving the same ideas such as insurance or calculating the MTBF of something).

While I could just about dredge up enough maths from 25 years ago to solve it, I'm not convinced that there's a real-life application for using quadratics to prove that n² - n = 90.

Working out how many sweets there are, or working out what the probability of your hard drive failing before the warranty ends is, or working out whether you'll pay more than your payout in increased premiums if you make an insurance claim, sure - but real life would make you use the quadratics on the way to a number, not to a proof.

I'm quite happy with it as part of an exam paper, as effectively a mathematical game, but I don't think it's anywhere close to a real-world example in its current form.

red marley · « **Reply #12 on:** 09 June, 2015, 08:34:31 am »

I think in this case the n²-n = 90 is just to make the question easier. They could have just asked how many sweets in the bag, but by presenting the quadratic it gives a little guidance as how to proceed.

In my view, what makes this a good applied question is that it demonstrates that something seemingly impossible at first glance, is solvable by breaking it down into simpler steps. It demonstrates why rearranging equations or solving quadratics or using rules of probability are helpful things to learn. It motivates a useful generalisable set of skills.

clarion · « **Reply #13 on:** 09 June, 2015, 09:03:17 am »

Hannah's sweets is a pretty straightforward problem. I like the witty way it is presented, with a punchline (which actually helps the student).

And wot jo sed.

Cudzoziemiec · « **Reply #14 on:** 09 June, 2015, 10:37:31 am »

The odd one out question would be good if you had to give a reason.

mrcharly-YHT · « **Reply #15 on:** 09 June, 2015, 01:27:15 pm »

I couldn't remember anything about probability - but the students should have been tutored in that.

The odd one out is more of a philosophical question (and those both irritate and interest me).

anyone solved the problem part way down the page, the one with columns of numbers? I have a migraine coming on and can't think straight.

clarion · « **Reply #16 on:** 09 June, 2015, 04:04:47 pm »

It's easier if you give up and colour it in.

Ham · « **Reply #17 on:** 09 June, 2015, 04:51:34 pm »

If I hadn't known preschool children could answer it might have taken me longer than about a minute. You can answer it, too

Kim · « **Reply #18 on:** 09 June, 2015, 05:16:25 pm »

Solved it.

(click to show/hide)

Cudzoziemiec · « **Reply #19 on:** 09 June, 2015, 07:08:42 pm »

Ah ha! Or even,

(click to show/hide)

Wowbagger · « **Reply #20 on:** 09 June, 2015, 07:58:28 pm »

HULL CITY.

mrcharly-YHT · « **Reply #21 on:** 09 June, 2015, 08:04:20 pm »

Doh - now I see it.

Bloody nothing to do with maths

red marley · « **Reply #22 on:** 09 June, 2015, 08:44:34 pm »

That's the point. The article is about how typically these kinds of 'logic problems' often penalise creative, lateral thinking even though that can be an important skill in problem solving.

Cudzoziemiec · « **Reply #23 on:** 10 June, 2015, 10:56:00 am »

Quote from: Wowbagger on 09 June, 2015, 07:58:28 pm

HULL CITY.

<Eurovision>Norway.

mrcharly-YHT · « **Reply #24 on:** 10 June, 2015, 11:05:13 am »

Quote from: Cudzoziemiec on 10 June, 2015, 10:56:00 am

Quote from: Wowbagger on 09 June, 2015, 07:58:28 pm
HULL CITY.
<Eurovision>Norway.

Is this another logic puzzle or are we playing eurovision Mornington Cresent?

Author Topic: Another pair of kids' logic problems (Read 8384 times)

red marley

red marley

red marley