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## #1 2013-06-19 18:35:53

Kapabhi
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Registered: 2013-06-19
Posts: 4

"seventy dollars,"said the rector."that's whats i want you children to spend at the bazaar .

"i'm told that there are five stalls,at which the prices are 1,2,3,4,and 5 dollars respectively. I want each of you to bring back three presents for your mother."

"not necessarily,"said the rector."But each of you must patronize two stalls;and you must not,collectively,patronize more than three stalls in all. Also you must so divide the money that no two of you spend the same amount and that no one spends as much as fourteen dollars."HOW MANY CHILDREN WENT TO THE BAZAAR?
AND WHICH STALLS DID THE PATRONIZE?

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## #2 2013-06-19 18:56:15

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,833
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http://www.mathisfunforum.com/misc.php?action=rules

There is no point on bumping your thread, people need some time to find it out.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #3 2013-06-19 18:58:42

Kapabhi
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Registered: 2013-06-19
Posts: 4

Sorry.

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## #4 2013-06-19 19:03:44

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,833
Website

Its ok

I hope someone will solve this soon.

BTW what happens to one when he patonises a shop? I mean would you make it a little clear?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #5 2013-06-19 19:12:28

Kapabhi
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Registered: 2013-06-19
Posts: 4

*And which stalls did the children patronize?

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## #6 2013-06-19 19:49:54

bob bundy
Registered: 2010-06-20
Posts: 8,085

hi Kapabhi

Welcome to the forum.

I cannot see a nice simple algebraic way to do this.  Too many variables.

LATER EDIT:

I find this puzzle is impossible.  It may be that I am misunderstanding the rules.  It wouldn't be the first time.

explanation:

Let number of children be n.

\$70 to spend and each spend < \$14  => n > 5

They must go to 3 stalls; let's call them a, b and c.

Each must buy three presents, but only from two of these three.  So the options are

aab
aac
bba
bbc
cca
ccb

If these amounts of spending are to be different each child must pick one of the six.  => n = 6

If the stalls visited are 5, 4 and 3, (the most expensive stalls) then the individual spending options are

554 = 14
553 = 13
445 = 13
443 = 11
335 = 11
334 = 10

But they must spend different amounts, so this option this not possible.

try 5 4 2 (Note I have reduced the amount by the smallest amount)

554 = 14
552 = 12
445 = 13
442 = 10
225 = 9
224 = 8

These are all different but they sum to only 66, so we cannot spend all the money.

Any further reduction will lead to totals lower than \$66.

Looks like n = 6 won't work.

?????

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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## #7 2013-06-19 21:38:43

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

Thinking about it, there will always be exactly 6 ways of patronising the stalls, so n=6 must work for some set of stalls. Also, none of the children may spend 14 dollars, so, the combination 554 is out of the question. So, We cannot have both 5 and 4 patronised.

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 2013-06-19 21:43:53

bob bundy
Registered: 2010-06-20
Posts: 8,085

hi Stefy,

Glad you're 'on the case'.  I've just edited my post, proving it is impossible.  ??

What do you think?

LATER EDIT:  I have a solution for \$60.

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 2013-06-19 21:50:26

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

There must be something in the wording we are misinterpreting. Maybe each child is allowed to patronise 3 different stalls. In that case 5,3,2 and n=7 is a solution

Edit: I do too. It's the 532 case.

Last edited by anonimnystefy (2013-06-19 21:52:47)

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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## #10 2013-06-20 00:49:14

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

I can't find a solution to the puzzle as it stands.

Last edited by phrontister (2013-06-20 01:02:13)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #11 2013-06-20 01:04:27

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

What happened?

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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## #12 2013-06-20 01:08:32

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Rushed it and allowed a rogue fourth digit to sneak in.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #13 2013-06-20 01:11:49

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

It happens.

I have a feeling that the fix above is the one that should do the job, but, we'll just have to wait for the OP to come back and clarify.

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 2013-06-20 01:51:02

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Yes, I agree with all of that.

Edit: I muffed this next bit...(see post #16, #20 & #22)
Also, the \$60 fix gives a unique solution but increasing the number of patronised stalls to 3 gives multiple solutions.

Last edited by phrontister (2014-06-03 02:55:54)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #15 2013-06-20 01:52:37

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

Which?

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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## #16 2013-06-20 02:07:37

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

No...I messed that up too. I was looking at the \$60 scenario still - where it does apply - and didn't think to check it out for \$70 - where it doesn't apply. I should have stayed out tonight (had supper with friends) and not come home so early!

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #17 2013-06-20 02:10:50

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

So, both fixes are fine.

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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## #18 2013-06-20 02:19:58

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

anonimnystefy wrote:

So, both fixes are fine.

Is this one of them?

Maybe each child is allowed to patronise 3 different stalls. In that case 5,3,2 and n=7 is a solution

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #19 2013-06-20 02:24:03

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

Yup.

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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## #20 2013-06-20 02:24:17

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Hang on...just realised my post #16 is wrong too (I think), but I have to do something for a while first and then I'll check it out properly. Not thinking straight right now, and still rushing.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #21 2013-06-20 02:27:09

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

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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## #22 2013-06-20 03:15:51

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Back again...

Yes, I see now what I did. Forget everything I said about multiple solutions, as that just doesn't make sense (I shouldn't have had that extra cup of tea).

And yes, both fixes are fine. Phew...finally got there!

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #23 2013-06-20 03:56:51

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

phrontister wrote:

Back again...

Yes, I see now what I did. Forget everything I said about multiple solutions, as that just doesn't make sense (I shouldn't have had that extra cup of tea).

And yes, both fixes are fine. Phew...finally got there!

Are you sure it was tea you were drinking?

Great! Now we can wait for the OP to confirm if one of the two is what he wanted.

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 2013-06-20 04:05:54

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

anonimnystefy wrote:

Are you sure it was tea you were drinking?

Yes, but maybe the hostess put in two teaspoons of sugar instead of one, and that addled my brain. I don't drink alcohol, so I couldn't have been under the affluence of incohol.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #25 2013-06-20 04:25:13

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