=IF(OR($B2=”DS”,$B2=”Manual”)=TRUE,IF($B2=”DS”,IF($C2=”Price”,OFFSET(‘DS Data’!D$1,MATCH($D2,’DS Data’!$B$2:$B$1048576,0),0)/OFFSET(‘DS Data’!C$1,MATCH($D2,’DS Data’!$B$2:$B$1048576,0),0)-1,OFFSET(‘DS Data’!C$1,MATCH($D2,’DS Data’!$B$2:$B$1048576,0),0)/1200),IF($C2=”Price”,OFFSET(‘Manual Data’!$A$2,MATCH(E$1,’Manual Data’!$A$3:$A$1048576,0),MATCH($A2,’Manual Data’!$B$1:$XFD$1,0))/OFFSET(‘Manual Data’!$A$2,MATCH(E$1,’Manual Data’!$A$3:$A$1048576,0)-1,MATCH($A2,’Manual Data’!$B$1:$XFD$1,0))-1,OFFSET(‘Manual Data’!$A$2,MATCH(E$1,’Manual Data’!$A$3:$A$1048576,0)-1,MATCH($A2,’Manual Data’!$B$1:$XFD$1,0))/1200)),ERROR.TYPE(1))

For 16 values, there are 2^16=65536 combinations, equal to the number of rows in Excel 2003. Each combination is tested by calculating the difference (scaled up and rounded) and then adding on the position index. The results are passed to SMALL(.,B1), which returns the smallest combination of difference and position index. Changing B1 to 2 returns the next smallest combination etc.

In the Excel 2010 beta this more flexible (though even more incoherent!) version seems to work, which extends to up to 20 test values.

=MOD(MOD(SMALL(ABS(ROUND((MMULT(INT(MOD(ROW(A1:INDEX(A:A,2^ROWS(A2:A17)))
/2^TRANSPOSE((ROW(A2:A17)-ROW(A2))),2)),A2:A17)-A1)*10^9,-7))+
ROW(A1:INDEX(A:A,2^ROWS(A2:A17))),B1),10^7)/2^(ROW(A2:A17)-ROW(A2)),2)>=1

The MMULT function works for larger ranges now apparently, don’t know about Excel 2007?

For 16 values, there are 2^16=65536 combinations, equal to the number of rows in Excel 2003. Each combination is tested by calculating the difference (scaled up and rounded) and then adding on the position index. The results are passed to SMALL(.,B1), which returns the smallest combination of difference and position index. Changing B1 to 2 returns the next smallest combination etc.

In the Excel 2010 beta this more flexible (though even more incoherent!) version seems to work, which extends to up to 20 test values.

=MOD(MOD(SMALL(ABS(ROUND((MMULT(INT(MOD(ROW(A1:INDEX(A:A,2^ROWS(A2:A17)))
/2^TRANSPOSE((ROW(A2:A17)-ROW(A2))),2)),–A2:A17)-A1)*10^9,-7))+
ROW(A1:INDEX(A:A,2^ROWS(A2:A17))),B1),10^7)/2^(ROW(A2:A17)-ROW(A2)),2)>=1

The MMULT function works for larger ranges now apparently, don’t know about Excel 2007?

Can you explain in a little more detail what your formula is calculating? It looks like it is identifying the values in A2:A17 that, when added together, will total up to (could be less), but no more than, the target value… if that is the case, then what is the value in B1 for/doing?

=MOD(MOD(SMALL(ABS(ROUND((
(MOD(ROW(A:A)/2^0,2)>=1)*A2+
(MOD(ROW(A:A)/2^1,2)>=1)*A3+
(MOD(ROW(A:A)/2^2,2)>=1)*A4+
(MOD(ROW(A:A)/2^3,2)>=1)*A5+
(MOD(ROW(A:A)/2^4,2)>=1)*A6+
(MOD(ROW(A:A)/2^5,2)>=1)*A7+
(MOD(ROW(A:A)/2^6,2)>=1)*A8+
(MOD(ROW(A:A)/2^7,2)>=1)*A9+
(MOD(ROW(A:A)/2^8,2)>=1)*A10+
(MOD(ROW(A:A)/2^9,2)>=1)*A11+
(MOD(ROW(A:A)/2^10,2)>=1)*A12+
(MOD(ROW(A:A)/2^11,2)>=1)*A13+
(MOD(ROW(A:A)/2^12,2)>=1)*A14+
(MOD(ROW(A:A)/2^13,2)>=1)*A15+
(MOD(ROW(A:A)/2^14,2)>=1)*A16+
(MOD(ROW(A:A)/2^15,2)>=1)*A17
-A1)*10^8,-6))+ROW(A:A),B1),10^6)/2
^(ROW(A2:A17)-ROW(A2)),2)>=1

Put a target value in A1, values to sum in A2:A17, and B1=1.
Select B2:B17 and array-enter this formula with {Ctrl+Shift+Enter}.

It takes a few seconds to run, you can try B1=2,3,.. for other solutions.
Two decimal places accuracy is assumed.

I don’t think it’s possible to do in many less characters than this (568).
It could be extended to up to 20 values in Excel 2007+ (~690). lhm

=+TREND(OFFSET($J$6,+MATCH($C7,$J$7:$J$16,1),+MATCH($D7,OFFSET($K$6:$P$6,MATCH($C7,$J$7:$J$16,1)-1,0)),1,2),OFFSET($J$6,+MATCH($C7,$J$7:$J$16,1)-1,+MATCH($D7,OFFSET($K$6:$P$6,MATCH($C7,$J$7:$J$16,1)-1,0)),1,2),$D7)

Noting that it isn’t padded out with page names, yet !

It calculates a new Y value for a given X value between a set of X and Y Co-ordinates in an Array which can be in different locations based on 2 other variables (I think that’s what it did)

=IF(OR(Main!D77=Options!$F$14,Main!D77=Options!$F$15,Main!D77=Options!$F$16,Main!D77=Options!$F$17,Main!D77=Options!$F$18,Main!D77=Options!$F$19),0,IF(Main!D77?”,SUM(VALUE(LEFT(Main!D77,FIND(Options!$F$11,Main!D77)-1))*256,IF(Options!$D$7=”Y”,VALUE(MID(Main!D77,FIND(Options!$F$11,Main!D77,1)+1,FIND(Options!$F$11,(SUBSTITUTE(Main!D77,Options!$F$11,”X”,1)))-FIND(Options!$F$11,Main!D77,1)-1))*16,VALUE(RIGHT(Main!D77,LEN(Main!D77)-FIND(Options!$F$11,Main!D77)))*16),IF(Options!$D$7=”Y”,RIGHT(Main!D77,LEN(Main!D77)-FIND(Options!$F$11,(SUBSTITUTE(Main!D77,Options!$F$11,”X”,1)),1)),0)),0))

I wrote it as part of an angling match result calculator. The actual spreadsheet contains this formula in 50 rows x 50 columns.

Here’s the formula:

=IF(D8Assumptions!$C$39),(Assumptions!$C$39*Assumptions!$D$39)+((‘volumes including CFS’!D8-Assumptions!$C$39)*Assumptions!$D$40),IF(AND(‘volumes including CFS’!D8Assumptions!$C$40),(Assumptions!$C$39*Assumptions!$D$39)+((Assumptions!$C$40-Assumptions!$C$39)*Assumptions!$D$40)+((‘volumes including CFS’!D8-Assumptions!$C$40)*Assumptions!$D$41),(Assumptions!$C$39*Assumptions!$D$39)+((Assumptions!$C$40-Assumptions!$C$39)*Assumptions!$D$40)+((Assumptions!$C$41-Assumptions!$C$40)*Assumptions!$D$41)+((‘volumes including CFS’!D8-Assumptions!$C$41)*Assumptions!$D$42))))

It’s “only” 741 characters.

The formula implements a very standard “tiered pricing” formula, where the marginal price at each tier is lower as the total volume increases.

I found the bug by trying to simplify the formula. Here’s my first marginal improvement:

=IF(D8Tier1Threshold),(Tier1Threshold*Tier1Price)+((D8-Tier1Threshold)*Tier2Price),IF(AND(D8Tier2Threshold),(Tier1Threshold*Tier1Price)+((Tier2Threshold-Tier1Threshold)*Tier2Price)+((D8-Tier2Threshold)*Tier3Price),(Tier1Threshold*Tier1Price)+((Tier2Threshold-Tier1Threshold)*Tier2Price)+((Tier3Threshold-Tier2Threshold)*Tier3Price)+((D8-Tier3Threshold)*Tier4Price))))

This helps a little bit I guess.

To make a significant improvement I substituted a VLOOKUP as follows:

=VLOOKUP(D8,Residency_Pricing_Table,4,TRUE)+(D8-VLOOKUP(D8,Residency_Pricing_Table,2,TRUE))*VLOOKUP(D8,Residency_Pricing_Table,3,TRUE)

It must be paired with the following table, with a range name “Residency_Pricing_Table”:

Account Tier Lower
Range Boundary Rate Cum Cost
0 0 0.0300 0
4,500,000 4,500,000 0.0250 135,000.00
6,000,000 6,000,000 0.0200 172,500.00
9,000,000 9,000,000 0.0150 232,500.00

I think this is a vast improvement. However, I went one step further. The final version of the formula looks like this:

=TieredPrice(D8,Residency_Pricing_Table)

The User Function is:

Function TieredPrice(number, rngInput As Range)
Application.Volatile
‘
‘ A Tiered Pricing Table always has four columns:
‘ 1: the vlookup column, tier lower boundary
‘ 2: = col 1, data as the tier lower boundary
‘ 3: the tier marginal price
‘ 4: the cumulative cost up to the lower boundary of the tier
‘
‘ The table can have any number of rows (tiers)
‘
CumCost = Application.WorksheetFunction.VLookup(number, rngInput, 4, True)
NumInTier = number – Application.WorksheetFunction.VLookup(number, rngInput, 2, True)
CostInTier = NumInTier * Application.WorksheetFunction.VLookup(number, rngInput, 3, True)

TieredPrice = CumCost + CostInTier
End Function

The erroneous spreadsheet had tiered pricing formulas for many different components. The beauty of this function is that it works for any tiered formula, regardless of the number of tiers. Just pass the named range for the formula table to the function.

Soapbox comment: I believe there is never justification for a long, complex formula. Every effort should be made to simplify – often with User Functions. (I suppose the “final” version of a spreadsheet that must be optimized for speed would be a valid exception. But what spreadsheet is ever final?)

Regards,
Vin Underwood

i want to find the total number of bills i paid for a certain month

example:

I paid a bill on 10-Oct-06, 13-Oct-06, 17-Oct-06 & 27-Oct-06. There has to be some formula out there in which i can somehow enter >= 01-Oct-06 &