Firstly, we have an array of predetermined factors, ie. V-Z;
their attributes are 3, the first two (•xM) multiplied giving the 3rd.
f ... factors
• ... cap, the values in the data set may increase max
m ... fixed multiplier
p ... let's call it power
This is a separate, standalone array .. we'd access with eg. VLOOKUP
f • m pwr
V 1 9 9
W 2 8 16
X 3 7 21
Y 4 6 24
Z 5 5 25
—————————————————————————————————————————————
Then we have 6 columns, in which the actual data to be processed is in, & thereof derive the next-level result, based on the interaction of both samples introduced.
In addition, there are added two columns, for balance & profit.
Here's a short, 6-row data sample:
f • m bal profit
V 2 3 377 1
Y 2 3 156 7
Y 1 1 122 0
X 1 2 -27 2
Z 3 3 223 3
—————————————————————————————————————————————
Ultimately, starting at the end, we are comparing IF -27 inverted → so 27 is within the X's power range ie. 21 (as per the first sample) .. which is then fed into a bigger formula, beyond the scope of this post.
This can be done with VLOOKUP, all fine by now.
—————————————————————————————————————————————
To get to that .. for the working example, we are focusing coincidentally on row5, since that's the one with the first negative value in the 'balance' column, so ..
on factorX = which factor exactly is to us unknown &
balance -27 = which we have to locate amongst potentially dozens to hundreds of rows.
Why!?
Once we know that the factor is X, based on the * & multiplier pertaining to it, then we also know which 'power' (top array) to compare -27, as the identified first negative value in the balance column, to.
Is that clear?
I'd like to know the formula on how to achieve that, & (get to) move on with the broader-scope work.
—————————————————————————————————————————————
The main issue for me is not knowing how to identify the first negative or row -27 pertains to, then having that piece of information how to leverage it to get the X or identify the factor type, especially since its positioned left of the latter & to the best of my knowledge I cannot use negative column index number (so, latter even if possible is out of the question anyway).
To recap;
IF(21>27) = IF(-21<-27)
27 → LOCATE ROW with the first negative number (-27)
21 → IDENTIFY the FACTOR TYPE, same row as (-27)
→ VLOOKUP pwr, based on factor type identified (top array, 4th column right)
→ invert either 21 to a negative number or (-27) to the positive number
= TRUE/FALSE
Guessing your columns I'll say your first chart is in columns A to D, and the second in columns G to K
You could find the letter of that factor with something like this:
=INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0)))
INDEX(J:J<0) converts that column to TRUE and FALSE depending on being negative or not and with XMATCH you find the first TRUE. You could then use that in VLOOKUP:
=VLOOKUP(INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0))),A:D,4,0)
That would return the 21. You can use the first concept too to find the the -27 and with ABS have its "positive value"
=VLOOKUP(INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0))),A:D,4,0) > INDEX(J:J,XMATCH(TRUE,INDEX(J:J<0)))
That should return true or false in the comparison
Consider the following sheet/table:
A B
1 90 71
2 40 25
3 60 16
4 110 13
5 87 82
I want to have a general formula in cell C1 that sums the greatest value in column A (which is 110), plus the sum of the other values in column B (which are 71, 25, 16 and 82). I would appreciate if the formula wasn't an array formula (as in requiring Ctrl + Shift + Enter). I don’t have Office 365, I have Excel 2019.
My attempt
Getting the greatest value in column A is easy, we use MAX(A1:A5).
So the formula I want in cell C1 should be something like:
=MAX(A1:A5) + SUM(array_of_values_to_be_summed)
Obtaining the values of the other rows in column B (what I called array_of_values_to_be_summed in the previous formula) is the hard part. I've read about using INDEX, MATCH, their combination, and obtaining arrays by using parenthesis and equal signs, and I've tried that, without success so far.
For example, I noticed that NOT((A1:A5 = MAX(A1:A5))) yields an array/list containing ones (or TRUEs) for the relative position of the rows to be summed, and containing a zero (or FALSE) for the relative position of the row to be omitted. Maybe this is useful, I couldn't find how.
Any ideas? Thanks.
Edit 1 (solution)
I managed to obtain what I wanted. I simply multiplied the array obtained with the NOT formula, by the range B1:B5. The final formula is:
=MAX(A1:A5) + SUM(NOT((A1:A5 = MAX(A1:A5))) * B1:B5)
Edit 2 (duplicate values)
I forgot to explain what the formula should do if there are duplicates in column A. In that case, the first term of my final formula (the term that has the MAX function) would be the one whose corresponding value in column B is smallest, and the value in column B of the other duplicates would be used in the second term (the one containing the SUM function).
For example, consider the following sheet/table:
A B
1 90 71
2 110 25
3 60 16
4 110 13
5 110 82
Based on the above table, the formula should yield 110 + (71 + 25 + 16 + 82) = 304.
Just to give context, the reason I want such a formula is because I’m writing a spreadsheet that automatically calculates the electric current rating of the short-circuit protective device of the feeder of a group of electric motors in a house or building or mall, as required by the article 430.62(A) of the US National Electrical Code. Column A is the current rating of the short-circuit protective device of the branch-circuit of each motors, and column B is the full-load current of each motor.
You can use this formula
=MAX(A1:A5)
+SUM(B1:B5)
-AGGREGATE(15,6,(B1:B5)/(A1:A5=MAX(A1:A5)),1)
Based on #Anupam Chand's hint for max-value-duplicates there could also be min-value-duplicates in column B for corresponding max-value-duplicates in column A. :) This formula would account for that
=SUM(B1:B5)
+(MAX(A1:A5)-AGGREGATE(15,6,(B1:B5)/(A1:A5=MAX(A1:A5)),1))
*SUMPRODUCT((A1:A5=MAX(A1:A5))*(B1:B5=AGGREGATE(15,6,(B1:B5)/(A1:A5=MAX(A1:A5)),1)))
Or with #Anupam Chand's shorter and better readable and overall better style :)
=SUM(B1:B5)
+(MAX(A1:A5)-MINIFS(B1:B5,A1:A5,MAX(A1:A5)))
*COUNTIFS(A1:A5,MAX(A1:A5),B1:B5,MINIFS(B1:B5,A1:A5,MAX(A1:A5)))
The explanation works for bot solutions:
The SUM-part just sums the whole list.
The second line gets the max-value for column A and the corresponding min-value of column B for the max-values in column A and adds or subtracts it respectively.
The third line counts, how many times the corresponding min-value for the max-value occurs and multiplies it with the second line.
Can you try this ?
=MAX(A1:A5)+SUM(B1:B5)-MINIFS(B1:B5,A1:A5,MAX(A1:A5))
What we're doing is adding the max of A to all rows of B and then subtracting the min value of B where A is the max.
If you have Excel 365 you can use the following LET-Formula
=LET(A,A1:A5,
B,B1:B5,
MaxA,MAX(A),
MinBExclude, MINIFS(B,A,MaxA),
sumB1,SUMPRODUCT(B*(A=MaxA)*(B<>MinBExclude)),
sumB2,SUMPRODUCT(B*(A<>MaxA)),
MaxA +sumB1+sumB2
A and B are shortcuts for the two ranges
MaxA returns the max value for A (110)
MinBExclude filters the values of column B by the MaxA-value (25, 13, 82) and returns the min-value of the filtered result (13)
sumB1 returns the sum of the other MaxA values from column B (26 + 82)
sumB2 returns the sum of the values from B where value in A <> MaxA (71 + 60)
and finally the result is returned
If you don't have Excel 365 you can add helper columns for MaxA, MinBExclude, sumB1 and sumB2 and the final result
I'm trying to write formulae that will split a given number into the sum of 4 other numbers.
The other numbers are 100,150,170 and 200 so the formula would be
x = a*100+b*150+c*170+d*200 where x is the given number and a,b,c,d are integers.
My spreadsheet is set up as where col B are x values, and C,D,E,F are a,b,c,d respectively (see below).
B | C | D | E | F |
100 1 0 0 0
150 0 1 0 0
200 0 0 0 1
250 1 1 0 0
370 0 0 1 1
400 0 0 0 2
I need formulae for columns C,D,E,F (which are a,b,c,d in the formula)
Your help is greatly appreciated.
UPDATE:
Based on the research below, for input numbers greater than 730 and/or for all actually divisible input numbers use the following formulas:
100s: =CHOOSE(MOD(ROUNDUP([#number]/10;0); 20)+1;
0;1;1;0;1;1;0;1;0;0;1;0;0;1;0;0;1;0;1;1)
150s: =CHOOSE(MOD(ROUNDUP([#number]/10;0); 10)+1;
0;0;1;1;0;1;1;0;0;1)
170s: =CHOOSE(MOD(ROUNDUP([#number]/10;0); 5)+1;
0;3;1;4;2)
200s: =CEILING(([#number]-930)/200;1) +
CHOOSE(MOD(ROUNDUP([#number]/10;0); 20)+1;
4;1;2;0;2;3;1;3;1;2;4;2;3;0;2;3;0;3;0;1)
MOD(x; 20) will return numbers 0 - 19, CHOOSE(x;a;b;...) will return n-th argument based on the first argument (1=>second argument, ...)
see more info about CHOOSE
use , instead of ; based on your Windows language®ion settings
let's start with the assumption that you want to preferably use 200s over 170s over 150s over 100s - i.e. 300=200+100 instead of 300=2*150 and follow the logical conclusions:
the result set can only contain at most 1 100, at most 1 150, at most 4 170s and unlimited number of 200s (i started with 9 170s because 1700=8x200+100, but in reality there were at most 4)
there are only 20 possible subsets of (100s, 150s, 170s) - 2*2*5 options
930 is the largest input number without any 200s in the result set
based on observation of the data points, the subset repeats periodically for
number = 740*k + 10*l, k>1, l>0 - i'm not an expert on reverse-guessing on periodic functions from data, but here is my work in progress (charted data points are from the table at the bottom of this answer)
the functions are probably more complicated, if i manage to get them right, i'll update the answer
anyway for numbers smaller than 740, more tweaking of the formulas or a lookup table are needed (e.g. there is no way to get 730, so the result should be the same as for 740)
Here is my solution based on lookup formulas:
Following is the python script i used to generate the data points, formulas from the picture and the 60-row table itself in csv format (sorted as needed by the match function):
headers = ("100s", "150s", "170s", "200s")
table = {}
for c200 in range(30, -1, -1):
for c170 in range(9, -1, -1):
for c150 in range(1, -1, -1):
for c100 in range(1, -1, -1):
nr = 200*c200 + 170*c170 + 150*c150 + 100*c100
if nr not in table and nr <= 6000:
table[nr] = (c100, c150, c170, c200)
print("number\t" + "\t".join(headers))
for r in sorted(table):
c100, c150, c170, c200 = table[r]
print("{:6}\t{:2}\t{:2}\t{:2}\t{:2}".format(r, c100, c150, c170, c200))
__________
=IF(E$1<740; 0; INT((E$1-740)/200))
=E$1 - E$2*200
=MATCH(E$3; table[number]; -1)
=INDEX(table[number]; E$4)
=INDEX(table[100s]; E$4)
=INDEX(table[150s]; E$4)
=INDEX(table[170s]; E$4)
=INDEX(table[200s]; E$4) + E$2
__________
number,100s,150s,170s,200s
940,0,0,2,3
930,1,1,4,0
920,0,1,1,3
910,0,0,3,2
900,1,0,0,4
890,0,1,2,2
880,0,0,4,1
870,1,0,1,3
860,0,1,3,1
850,1,1,0,3
840,1,0,2,2
830,0,1,4,0
820,1,1,1,2
810,1,0,3,1
800,0,0,0,4
790,1,1,2,1
780,1,0,4,0
770,0,0,1,3
760,1,1,3,0
750,0,1,0,3
740,0,0,2,2
720,0,1,1,2
710,0,0,3,1
700,1,0,0,3
690,0,1,2,1
680,0,0,4,0
670,1,0,1,2
660,0,1,3,0
650,1,1,0,2
640,1,0,2,1
620,1,1,1,1
610,1,0,3,0
600,0,0,0,3
590,1,1,2,0
570,0,0,1,2
550,0,1,0,2
540,0,0,2,1
520,0,1,1,1
510,0,0,3,0
500,1,0,0,2
490,0,1,2,0
470,1,0,1,1
450,1,1,0,1
440,1,0,2,0
420,1,1,1,0
400,0,0,0,2
370,0,0,1,1
350,0,1,0,1
340,0,0,2,0
320,0,1,1,0
300,1,0,0,1
270,1,0,1,0
250,1,1,0,0
200,0,0,0,1
170,0,0,1,0
150,0,1,0,0
100,1,0,0,0
0,0,0,0,0
Assuming that you want as many of the highest values as possible (so 500 would be 2*200 + 100) try this approach assuming the number to split in B2 down:
Insert a header row with the 4 numbers, e.g. 100, 150, 170 and 200 in the range C1:F1
Now in F2 use this formula:
=INT(B2/F$1)
and in C2 copied across to E2
=INT(($B2-SUMPRODUCT(D$1:$G$1,D2:$G2))/C$1)
Now you can copy the formulas in C2:F2 down all columns
That should give the results from your table