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#1 2012-04-24 22:11:35

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

School of Hard Sums

If you can get Dave tv then I recommend this programme on Mondays at 8pm.  Like most Dave programmes it is repeated many times during the week.

Meanwhile back to my problem.

One of the puzzles is this. 

A town has a grid road system and there are five groups of students at the grid locations shown in my diagram.  The red numbers show how many students there are at each location.  eg.  There are 5 students at (3,7).

The students want to meet up at a grid point.  They can only walk along the grid lines.  Where should they agree to meet so that the total distance walked by all 13 of them is a minimum?

Now Marcus du Sautoy poses this puzzle to  Dara O'Briain and Alex Horne.  He declares that Dara's answer is not correct.  I think he is wrong!

As Marcus (OBE) is a Professor of Mathematics at the University of Oxford I thought I'd better get a second opinion.

Anyone care to try the puzzle and help me out?

Bob  smile

View Image: Daras puzzle.gif

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#2 2012-04-24 22:17:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

Sure thing! Give us some time. smile


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2012-04-24 22:28:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Hi bob bundy;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2012-04-24 22:30:21

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

hi bobbym,

Thanks for joining in.  Please would you post the coordinates for this answer.

Thanks,

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2012-04-24 22:31:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

(3,5)


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2012-04-24 22:32:58

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

The smallest I have gotten so far is 58.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2012-04-24 22:34:40

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

Hi bobbym

For that point I get 58.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#8 2012-04-24 22:35:00

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

hi

(3,5)  ?

I make that a distance of 5 x 2 + 2 x 3 + 2 x 4 + 3 x 8 + 2 x 5 = 58.

Stefy:  What coordinates please?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2012-04-24 22:35:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Yes, 58 is smallest. there are 14 students not 13 as you indicate. (3,3) is the spot. Sorry, I did not see that earlier.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2012-04-24 22:37:06

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

I get 58 for:

(3,3)
(3,4)
(3,5)
(4,3)
(4,4)
(4,5)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#11 2012-04-24 22:38:29

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

How can I have missed that?  I'm sure that was how the puzzle was set and 13 was the number.  At no time did I bother to count them!

What are you getting for the distance for (3,3) ?

Oh I see 58.  I think I need glasses!

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2012-04-24 22:39:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Hi;

All of these are 58.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2012-04-24 22:43:13

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

There is a lot of them.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#14 2012-04-24 22:44:49

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

Ok.  Enough.  Thank you so much.

In the programme Marcus uses a 'method' to calculate the optimum position and declares it to be (5,5).  As it happens the guest Alex gets this and so is declared the winner.  Dara, the presenter, gets (5,3) and is declared wrong.

I agree that there are many possible best answers, all giving 58, so thank you for comfirming that.  I'm just wondering, in view of the 13, 14 doubt, whether I made up a student.  The programme is repeated tonight so I'm going to watch it again.  I'll post some more tomorrow.

Thank you for your help.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2012-04-24 22:45:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

No, just 9.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#16 2012-04-24 22:47:27

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

That is a lot,bobbym.

Okay,tell us what happened.Maybe we can sue them.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#17 2012-04-24 22:53:35

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

OK.  Now I'm admitting to being doubly stupid.

(i)  I recorded the programme on my pvr so I don't need to wait.

(ii) There are 13 students as shown on the revised diagram below.

So sorry.  shame

Bob

ps.  Tt's a good programme if you can get it.  There may be some U tube clips.

View Image: Dara 2.gif

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#18 2012-04-24 22:54:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Hi;

If you reduce the number of students at (3,7) to 4 you will get a unique answer.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#19 2012-04-24 22:55:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Mine is better, there are still 2 solutions!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#20 2012-04-24 22:57:05

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

Did you see post #17 ?

That's the corrected diagram.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#21 2012-04-24 22:59:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Hi;

I see it now there is only one solution now! Thanks for posting that.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#22 2012-04-24 23:00:03

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,168

Re: School of Hard Sums

Which is?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#23 2012-04-24 23:01:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

Hi Bob

I got 51 at (5,5).I think the guys who said that might be correct.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#24 2012-04-24 23:01:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: School of Hard Sums

Looks like (5,5) for 51.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#25 2012-04-24 23:05:31

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: School of Hard Sums

Yup.Since we got 58 everywhere,we just subtract the taxicab distance of the student who is alone from the total distance and we get that of all those that had the distance 58,the smallest one is when we subtract 7.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

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