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#1
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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. |
#2
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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. |
#3
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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. |
#4
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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. |
#5
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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 |
#6
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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. |
#7
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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 |
#8
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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 - |
#9
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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. |
#10
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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 |
#11
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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. |
#12
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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. |
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