Math Is Fun Forum

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Is this cool with you?

hi

so to pay them both out he could do it like this:(90,100)?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi;

That is amazing you started reading it one minute before I edited it. If you reread the problem you will see your present question does not apply.

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Is this cool with you?

hi

is (4,16,30) the same as (16,4,30)?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi;

I think order counts here. That represents 2 different ways to pay off the debt.

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

I'm getting a different answer.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Wait a minute!
I thought he was repaying them both in parallel.

Is it like:
He pays to A, and then B, then again A ...
He pays to B, and then again B, then A ...

Are these among the possibilities?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Yes, the order you pay, represents different arrangements. This is a very tough one.

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Is this cool with you?

so (10,10,10,10,10) would be diffferent from (10,10,10,10,10) because we can pay 1st 2nd and 3rd 10 to the first guy,or we could pay 1st 3rd and 5th ten to the first guy.that doesn't seem very logical if you write it as an ordered sequence.

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi;

Both of those are the same. I can not answer that question as to the why because that would give away the answer. Or at least give away a try at the 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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Is this cool with you?

but if the (10,10,10,10,10) is the same when the first two tens are flipped than shouldn't (14,6,30) be the sam as the triple with the first two flipped which is (6,14,30)

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Two of the same objects can not be flipped. There is only one way to throw a 12 with 2 dice. ( 6 , 6 ) you cannot flip that and say there are two ways. Now with 2 different numbers there are 2 ways to throw an eleven ( 6, 5 ) and ( 5 , 6 ).

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi,

I'm understanding this in a way different from the dice.

If it was paid in five instalments, it could be
A,A,B,B,B
A,B,A,B,B
B,A,B,B,A
etc.?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I believe those are all different. This one is hard even to keep straight in your head. I am getting confused.

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Okay.
Anywa, I'm starting with a small example.
Let me check that first.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Okay, take your time. I would like to see a simple solution to this.

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

In the problem, can you give some more examples how he can pay back?

...he could pay them both off at once ( 20 , 30 ) ...

Can he pay them together also? or is it strictly either (20,30) or (30,20)?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I can provide some actual numbers.

If my answers of a smaller problem are not enough then I will provide a clue that will explain most of it.

May I start with the numbers first?

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Okay.

Maybe you can start with (2,3) or (3,4) instead of (20,30), so that I may verify without a machine!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi;

I understand, this calculation is difficult even when you have the answer. Please give me some time to generate those.

(1,1) (he owes both one dollar) = 2 ways
(2,2) = 14 ways
(2,3) = 37 ways
(3,4) = 289 ways

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Thanks for the values.
It matches with those I calculated, I haven't done (3,4) yet, but I think I understood the problem.

The way is to pay one at a time, considering the partitions and order. Hmmm, nice!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

The solution I have is difficult. I am thinking partitions too, in order to shorten it.

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

If there's a sigle person to be paid back, answer is simply a power of 2,
for more persons it's tougher.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi gAr;

That is correct, for single persons.

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi,

This may take time I guess.
Not sure whether there can be a closed form.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I do not think so. Even the GF is difficult. I am looking for a recurrence.

---

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.