Number sortation
 

I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page, 1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and 8.

Number sortation
 

What happens if you have an odd number of pages to start with? Is it
increased by 1 to make it even?

Pete

On Oct 11, 10:38 pm, daffy1 wrote:
I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page, 1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and 8.

Number sortation
 

What if there is say 22 pages?

daffy1 wrote:

Sorry, I should have said that there is only even numbers to start with.

"Pete_UK" wrote:


What happens if you have an odd number of pages to start with? Is it
increased by 1 to make it even?

Pete

On Oct 11, 10:38 pm, daffy1 wrote:

I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page, 1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and 8.

Number sortation
 

The submitted pages must be a multiple of 4.

"Bob I" wrote:

What if there is say 22 pages?

daffy1 wrote:

Sorry, I should have said that there is only even numbers to start with.

"Pete_UK" wrote:


What happens if you have an odd number of pages to start with? Is it
increased by 1 to make it even?

Pete

On Oct 11, 10:38 pm, daffy1 wrote:

I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page, 1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and 8.

Number sortation
 

On Fri, 12 Oct 2007 08:26:01 -0700, daffy1
wrote:

The submitted pages must be a multiple of 4.

Then why isn't 4 one of the allowable dividers?
--ron

Number sortation
 

What is your logic for preferring 24+16+12, and not 24+20+8 (or 20+20+12, or
20+16+16, or ...)?
--
David Biddulph

"daffy1" wrote in message
...
I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.

Number sortation
 

For our machinery 4 is not an allowable divider.

"Ron Rosenfeld" wrote:

On Fri, 12 Oct 2007 08:26:01 -0700, daffy1
wrote:

The submitted pages must be a multiple of 4.

Then why isn't 4 one of the allowable dividers?
--ron

Number sortation
 

Assume B1 contains the sortation number (52 in your example).


B3=24 C3=Page
B4=20 C4=Page
B5=16 C5=Page
B6=12 C6=Page
B7=8 C7=Page

Use this formula in A3:
=INT(B1/B3)-IF(($B$1 - B3*INT(B1/B3))=4,1,0)

Use this formula in A4, and copy down to A5:A7
=INT(($B$1-SUMPRODUCT($A$3:A3,$B$3:B3))/B4)-IF(($B$1 - SUMPRODUCT($A
$3:A3,$B$3:B3))/B4=4,1,0)

Hope that works for you.



On Oct 12, 12:11 pm, daffy1 wrote:
For our machinery 4 is not an allowable divider.



"Ron Rosenfeld" wrote:
On Fri, 12 Oct 2007 08:26:01 -0700, daffy1
wrote:

The submitted pages must be a multiple of 4.

Then why isn't 4 one of the allowable dividers?
--ron- Hide quoted text -

- Show quoted text -

Number sortation
 

The order I am going by is taking the largest number first (24) and then the
next largest number (20). My original number combo was wrong. So yes, this
case submitting a 52 would result in a 24 + 20 = 8. My apologies for that
oversite.

"David Biddulph" wrote:

What is your logic for preferring 24+16+12, and not 24+20+8 (or 20+20+12, or
20+16+16, or ...)?
--
David Biddulph

"daffy1" wrote in message
...
I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.

Number sortation
 

Seems you then need to start by Subtracting the largest available
number, and work your way down.

daffy1 wrote:

For our machinery 4 is not an allowable divider.

"Ron Rosenfeld" wrote:


On Fri, 12 Oct 2007 08:26:01 -0700, daffy1
wrote:


The submitted pages must be a multiple of 4.

Then why isn't 4 one of the allowable dividers?
--ron

Number sortation
 

give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.

(ie 10110)

Hi. You mention "Only available..."

As a side note with your numbers, you selected the second of 13 possible
solutions. You may need to specify a more detailed "Rule".

FrobeniusSolve[{24,20,16,12,8},52]]

{1,1,0,0,1},
{1,0,1,1,0},
{1,0,0,1,2},
{0,2,0,1,0},
{0,1,2,0,0},
{0,1,1,0,2},
{0,1,0,2,1},
{0,1,0,0,4},
{0,0,2,1,1},
{0,0,1,3,0},
{0,0,1,1,3},
{0,0,0,3,2},
{0,0,0,1,5}

So one might think the solution is:
1*24 + 1*20 + 1*8 = 52
or
1*12+5*8 = 52
etc...

All numbers in {24,20,16,12,8} are Co-Prime, hence there are an infinite
number that can't be reproduced with these numbers.
Your page numbers can only be 8,12,16,20, ...(+4) multiples of 4.

Just to mention...
From Number Theory, if you could reduce the last page from 8 to 7, then the
Frobenius Number reduces from Infinity to 29.

FrobeniusNumber[{24,20,16,12,7}] = 29

(29 being the largest page # you can't do)
Therefore, every page number above 29 can be represented from
{24,20,16,12,7}. I don't know what your requirements are, but thought it
might be worth mentioning.

--
Dana DeLouis


"daffy1" wrote in message
...
I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.

Number sortation
 

Sorry to make a mess of this. My only "Rule" is that given the number 52 as
an example it would have to divide into 1*24 + 1*20 + 1*8.

"Dana DeLouis" wrote:

give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.

(ie 10110)

Hi. You mention "Only available..."

As a side note with your numbers, you selected the second of 13 possible
solutions. You may need to specify a more detailed "Rule".

FrobeniusSolve[{24,20,16,12,8},52]]

{1,1,0,0,1},
{1,0,1,1,0},
{1,0,0,1,2},
{0,2,0,1,0},
{0,1,2,0,0},
{0,1,1,0,2},
{0,1,0,2,1},
{0,1,0,0,4},
{0,0,2,1,1},
{0,0,1,3,0},
{0,0,1,1,3},
{0,0,0,3,2},
{0,0,0,1,5}

So one might think the solution is:
1*24 + 1*20 + 1*8 = 52
or
1*12+5*8 = 52
etc...

All numbers in {24,20,16,12,8} are Co-Prime, hence there are an infinite
number that can't be reproduced with these numbers.
Your page numbers can only be 8,12,16,20, ...(+4) multiples of 4.

Just to mention...
From Number Theory, if you could reduce the last page from 8 to 7, then the
Frobenius Number reduces from Infinity to 29.

FrobeniusNumber[{24,20,16,12,7}] = 29

(29 being the largest page # you can't do)
Therefore, every page number above 29 can be represented from
{24,20,16,12,7}. I don't know what your requirements are, but thought it
might be worth mentioning.

--
Dana DeLouis


"daffy1" wrote in message
...
I am trying to come up with a formula to sort page counts. Example: If I
give the number 52. It has to sort into 1 24-page, 0 20-page, 1 16-page,
1
12-page and 0 8 page. The only available dividers are 24, 20, 16, 12 and
8.