Homework, please help an idiot mother

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logic32
Posts: 177
Joined: Mon Jul 26, 2010 7:05 pm

Homework, please help an idiot mother

Post by logic32 »

I was wondering if any of you clever people can help me with my daughter's homework. We have been trying to work it out for about an hour and I now give up !

There are 4 jugs, one is a 9 litre ,then a 7 litre, a 4 litre and a 2 litre .
The 9 litre jug is full, the others are empty. We have to work out how to get 3 litres into 3 of the jugs.

Am I being stupid or is it not possible ?

Many thanks in advance of your cleverness !
ginx
Posts: 2151
Joined: Mon Jul 04, 2011 2:47 pm
Location: Warwickshire

Re: Homework, please help an idiot mother

Post by ginx »

I have no idea at all, but that sounds very much like an 11+ kind of question.

Sorry!
logic32
Posts: 177
Joined: Mon Jul 26, 2010 7:05 pm

Re: Homework, please help an idiot mother

Post by logic32 »

No just year 5 homework. Maths isn't exactly my strong point and despite the name nor is logic !!!
Minesatea
Posts: 1234
Joined: Sat Oct 31, 2009 12:08 am

Re: Homework, please help an idiot mother

Post by Minesatea »

According to DS (year 10)!
fill 7L jug from the 9L, 2 7 0 0
fill 4L jug from the 7L, 2 3 4 0
fill 2L jug from the 7L, 2 1 4 2
pour 2L into 9L, 4 1 4 0
pour 7L into the 2L, 4 0 4 1
fill 7 L with 4L and 9L, 1 7 0 1
fill 4L with 7L, 1 3 4 1
pour 4l into 9L, 5 3 0 1
pour 2L into 4L, 5 3 1 0
fill 2L from 9L, 3 3 1 2
pour 2L into 4L, 3 3 3 0
stevew61
Posts: 1786
Joined: Fri Nov 17, 2006 9:54 pm
Location: caversham

Re: Homework, please help an idiot mother

Post by stevew61 »

Not a full answer but a fudge.

Pour the full 9 fully into the 7. So 9 has two litres and 7 has seven litres.

Pour the 7 fully into the 4. So 7 has three and 4 has four litres.

Pour the 4 into the 2. So 4 and 2 both have two litres.

Now comes the fudge pour half of the 2 into the 9 makes three litres and pour the other half into the 4 makes three litres.

Drawing a diagram helps and if I had more time and patience maybe with a few more steps I could do it without a fudge. :lol:
Sally-Anne
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Joined: Wed Jan 11, 2006 8:10 pm
Location: Buckinghamshire

Re: Homework, please help an idiot mother

Post by Sally-Anne »

My DSs' maths teacher used to revel in setting problems like this.

We quite enjoyed solving them, but when it all got too much it was always "Google Is Your Friend". There is a useful visual representation of how to solve the problem here, http://nrich.maths.org/1977/solution" onclick="window.open(this.href);return false; . It confuses things a bit by talking about jugs of 8 litres, but otherwise it seems fairly clear.

But anyway, as far as I can see, minesateas' DS has cracked it as well. Take a gold star, that boy! :D
Okanagan
Posts: 1706
Joined: Mon Aug 22, 2011 9:20 pm
Location: Warwickshire

Re: Homework, please help an idiot mother

Post by Okanagan »

Code: Select all

step		                                                                                  9litre       7litre       4litre       2litre
1	fill the 4 litre jug from the 9 litre jug	                                             5            0            4            0
2	empty the 4 litre jug into the 7 litre jug	                                            5            4            0            0
3	fill the 4 litre jug from the 9 litre jug	                                             1            4            4            0
4	fill the 7 litre jug using 3 litres from the 4 litre jug	                              1            7            1            0
5	empty the remaining 1 litre in the 4 litre jug into the 2 litre jug                      1            7            0            1
6	fill the 4 litre jug from the 7 litre jug	                                             1            3            4            1
7	fill the 2 litre jug using 1 litre from the 4 litre jug	                               1            3            3            2
8	empty the 2 litre jug into the 9 litre jug	                                            3            3            3            0

There may be quicker ways!
logic32
Posts: 177
Joined: Mon Jul 26, 2010 7:05 pm

Re: Homework, please help an idiot mother

Post by logic32 »

Wow, I knew there would be lovely clever people on here.

Perhaps this homework has been set for my 9 year old to find out how intelligent the parents are as we clearly had to help. In my case a dismal fail...

Thank you so much !
JaneEyre
Posts: 4843
Joined: Sun May 09, 2010 1:04 pm

Re: Homework, please help an idiot mother

Post by JaneEyre »

logic32 wrote: There are 4 jugs, one is a 9 litre ,then a 7 litre, a 4 litre and a 2 litre .
The 9 litre jug is full, the others are empty. We have to work out how to get 3 litres into 3 of the jugs.
Okanagan wrote:

Code: Select all

step		                                                                                  9litre       7litre       4litre       2litre
1	fill the 4 litre jug from the 9 litre jug	                                             5            0            4            0
2	empty the 4 litre jug into the 7 litre jug	                                            5            4            0            0
3	fill the 4 litre jug from the 9 litre jug	                                             1            4            4            0
4	fill the 7 litre jug using 3 litres from the 4 litre jug	                              1            7            1            0
5	empty the remaining 1 litre in the 4 litre jug into the 2 litre jug                      1            7            0            1
6	fill the 4 litre jug from the 7 litre jug	                                             1            3            4            1
7	fill the 2 litre jug using 1 litre from the 4 litre jug	                               1            3            3            2
8	empty the 2 litre jug into the 9 litre jug	                                            3            3            3            0

There may be quicker ways!
Is there something missing in the question, some conditions about how the water is poured?

I have seen the link on nrich given by Sally-Anne and seen the brilliant work done by Mineatea’s DS (thousands bravos!), but why can’t we just leave aside the smallest jug holding just two litres as it will never hold 3 litres… And then we just pour from the largest jug 3l in second jug (which could hold 7l) and third jug (which could hold 4l) and then it’s job done as three jug contains three litres.
Why to go into complicated stuff?
I know… my reasoning is completely babyish :oops: :cry: … but I just can’t see why we couldn’t do that… Maybe I just need a goodnight sleep!! :lol: :lol:
Okanagan
Posts: 1706
Joined: Mon Aug 22, 2011 9:20 pm
Location: Warwickshire

Re: Homework, please help an idiot mother

Post by Okanagan »

The trick is to realise that you need to end up with 3 odd numbers. So 9 -(4*2) =1, (4*2)-7=1. Once you've got 1, 1 and 7 it's not too difficult to use the 2 litre jug to move it around in multiples of 2. A slightly easier to follow version with the same number of steps.

Code: Select all

step		                                                                                  9litre       7litre       4litre       2litre
1	fill the 4 litre jug from the 9 litre jug	                                             5            0            4            0
2	empty the 4 litre jug into the 7 litre jug	                                            5            4            0            0
3	fill the 4 litre jug from the 9 litre jug	                                             1            4            4            0
4	fill the 7 litre jug using 3 litres from the 4 litre jug	                              1            7            1            0
5	fill the 2 litre jug from the 7 litre jug	                                             1            5            1            2
6	empty the 2 litre jug into the 9 litre jug	                                            3            5            1            0
7	fill the 2 litre jug from the 7 litre jug	                                             3            3            1            2
8	empty the 2 litre jug into the 4 litre jug	                                            3            3            3            0
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