Tricky maths question

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Stuck

Tricky maths question

Post by Stuck »

This is a question from an independent school maths practise paper, my daughter cannot solve it and neither can I.

You are given a grid with 9 squares (3 across, 3 down etc). You have to insert the figures 2, 2, 2, 3, 3, 3, 4, 4, 4 - so that each line, including diagonally, adds up to nine. I can't do it. Is it a trick question or am I missing something?

Thank you.
Guest

Post by Guest »

I can do this so everything adds up except one diagonal. I can't get that last diagonal to add up to 9. Are you sure it included diagonals?
KenR
Posts: 1506
Joined: Fri Mar 17, 2006 6:12 pm
Location: Birmingham

Post by KenR »

The trick is to recognise that there are only 2 combinations of 3 numbers from the set that add up to 9, Either 2,3,4 or 3,3,3.

You need to recognise that having a different combination of 2,3 &4 in the rows (and columns ) will give the desired results for the rows and columns, but the only way the diagonals will add up to 9 is if one of these is 3, 3 & 3.

So start out by populating one of the diagonals with 3s and then just make sure the each of the rows has a different permutation. viz.

3xx
x3x
xx3

342
234
423

Ken
Guest

Post by Guest »

Absolutely sure about the diagonals, that is the problem we had as well. I think it might be a trick question, though nothing in the question gives a clue that it might be - I suppose it could be a mistake. It is from the Emmanuel school in London.
Guest

Post by Guest »

Thank you Ken R. I can't believe I never thought of that. You are brilliant!
Guest

Post by Guest »

well KenR aren't you the clever one. I'll have to try that question out on my little darling now.
KenR
Posts: 1506
Joined: Fri Mar 17, 2006 6:12 pm
Location: Birmingham

Post by KenR »

I've had lots of practice having gone through every paper I could find last year with my son. So I am fairly confident that I could now pass my 11+ second time round!

I found the Independent school exams are quite different to the normal 11+ grammar exams, the maths questions in particular seem to be graduated and get quite hard towards the end. I guess this is to test the scholarship level candidates.

I recall a practice paper we were sent from Solihull School last year which had a tough question about a boat and a hovercraft going in different directions and speeds around a lake. The candidates had to work out when the boat/hovercraft would pass and how far they had travelled.

The best way to work it out was by using algebra but strictly speaking they shouldn't have done this at KS2.
Guest55

Post by Guest55 »

The boat question can be done by thinking about relative speeds - if one is going 20 mph and the other 10 mph in the opposite direction they are approaching each other at 30 mph. So to meet you only have to think about one moving half way round at 30 mph - no algebra needed!
sj355
Posts: 1149
Joined: Thu Nov 02, 2006 4:07 pm
Location: Finchley - Barnet

Post by sj355 »

I gave this to my own little darling, who did it in less that 50 secs! :D I feel rather humilated for myself.... :shock:

INEX

Anonymous wrote:well KenR aren't you the clever one. I'll have to try that question out on my little darling now.
sj355
Guest

Post by Guest »

I've had lots of practice having gone through every paper I could find last year with my son. So I am fairly confident that I could now pass my 11+ second time round!
I gave this to both my little darlings (boys) and my big darling and all managed easily in under a minute. Maybe its just mum who's thick - despite a grammar school education!!
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