for the poorly educated among you (like Islet) my al Gebra post was pun on the fact that we inherited algebra from the Arabs

they developed it during the peak of their civilization, ~~ 1,000 AD

Post the 25 numbers and the amount paid and we'll figure it out.

I agree with doing some manual "prototypes" of this in Excel.

There is indeed a min. set that will satisfy your criteria & I don't think it will be in the millions. real issue is how many min. sets are there?

why not sort the 25 entries from largest to smallest; then copy the smallest 24 to a new worksheet; then copy 23... etc.

work back from there & rule out the small #'s - that should give at least one result

if not, keep track of it, and add back the biggest #, drop the 2nd biggest;

Lather/Rinse/Repeat

it's a weird Q. for me right now b/c I'm reading a book on Richard Feynmann and how when he was at Los Alamos, they set up "circles of girls on calculating machines" and ran things thru those circles until they got answers - and a bomb

I'd do a randomized approach.

1. Assign a random 0/1 value to each of the 25 Numbers
2. Add up the numbers with "1" value
3. If they add up to the goal value the you are set
4. If not cycle again

Leave the Excel woking all night and wake up to get the solution.

Post the numbers. I want to test my approach ;)

I am assuming this is for business deductions on a tax return...Here is the quick and dirty way I would do it:

1. Sort the receipts in column A
2. Add the receipts is column B
3. If yer lucky, one of the sums will be the exact number
4. If not lucky, select the receipts that get closest to the total
5. Call it a day, let the IRS figure the details out :D.

Good thing I am not a CPA :rolleyes:.

Amount paid from business checking = $1617.87
Charges:
486.87
32.48
247.84
9.64
27.19
30.00
79.36
28.17
119.53
26.79
530
141.65
11.4
40.83
53.15
36.93
11.40
84.25
44.39
58.25
328.53
175.82
182.44
332.67
3.87
-250.00 ... a $250 CREDIT from a return!

so far through trial and error I'm as close as 0.02

Here is your result:

486.87
32.48
247.84
9.64
27.19
30
79.36
28.17
119.53
26.79
530

That was easy my friend SmileWavy

I concur. At least that's a possible solution.

There might be other solutions, but since those were all grouped together on the top of the list, this has to be it.

Here's a link to an Excel template that does what you want. You will need the "Solver" add-in installed and enabled for it to work. I checked it out and it worked for me.
Excel Template - What Numbers In A Set Total A Target Value

Use the template I linked to and just let it run. It will run for about a minute.

486.87
27.19
79.36
28.17
530
11.4
40.83
11.4
44.39
175.82
182.44

There seems to be some funny accounting going on here. If you add up the first 11 items, they equal the exact amount paid on the business account. But if you look at my results, they also add up to the exact same amount. Do you want me to calculate the probability of that happening? Highly unlikely.

I think Aurel has it! She paid the balance toward the end of the month, but before the end of the statement period, so several of the later charges actually happened after my client made her payment.

I sent her a note asking which charges were tied to this payment. I'd expect she'll be able to confirm this eventually.

....use the Excel add-in programme called 'solver'....

easy peasy, lemon squeezy.......