I have 5 numbers and a total. How do I figure out the combination that will sum to the total?

Question

I have three checking acount deposits - $994.53 (solved), 1,545.05 & 1249.14. I believe that the checks that make up each deposit are in a combo of some or all of these amounts: $525.00 $1,249.14 $124.33 $128.83 $111.83 $90.97. I figured out by trial and error that the $994.53 deposit was 3 checks X $124.33 plus 2 checks X $128.83 plus 4 checks X $90.97 . Does any one know if there is an online calculator that can figure out the other two?

Answer 1

I don't know of any such calculator, but there's an algorithm you can use, of sorts, that should be methodical. I'd recommend using Excel to implement it.

What I'd do would be to take the deposit amount, and divide it by the largest check amount available:

1,545.05 / 1249.14 = 1, remainder 296.05

Then divide the remainder by the next largest check amount available:

296.05 / 128.83 = 2, remainder 38.39

That's too small to be covered by a check, so try the next largest check available:

296.05 / 124.33 = 2, remainder 47.39

Again too small... so try the next largest check available...

This is still trial and error, but at least it's a method instead of just guessing in the dark.

Excel has a Solver that you might be able to use for this...I can try to look into that...

OK, I figured out how to use Excel's Solver, and it was unable to find a solution for $1,545.05. I'm pretty sure I did it right, because I also had it solve for $994.53, and it got your answer in about 2 seconds. So I'd guess you'll never find an answer for $1,545.05.

The $1,249.14 one is trivial, since you have a check for that actual amount.