Excel: Decomposing numbers into sum of smaller numbers

Question

This is a real world use case: I have a home gym with different weighting disks (1.25 kg, 5 kg, 10 kg etc).

I have created an excel spreadsheet that calculates the weight that i should lift per exercise, as an example:

My question is: how can I get Excel to automatically decompose each cell into the appropiate disks that I should put on the bar? This is limited by the number of disks per disks weight (I don't have an infinite amount of 1 kg disks)

Example:

On the first cell we have 55 (kg). Since I have 2 disks of 25 kg at home and multiple 5 kg disks, I would like Excel to output 25x2 + 5 .

15x2 + 10x2 + 2.5x2 would also work but it's much more inefficient, so what I'd like to get is the solution with the least amount of different disks.

Answer 1

Check out the MOD() and QUOTIENT() functions and set up a nested IF statement with the various weights you have available.

Eg, using your example with "weight" to be made with 25 and 5 kg weights, something like

=QUOTIENT(Weight,25) & " 25 kg weights" & IF(MOD(Weight,25)>0," and " & QUOTIENT(MOD(Weight,25),5) & " 5 kg weights ","") 

Answer 2

Here is a link with several solutions for your problem.
https://www.extendoffice.com/documents/excel/3557-excel-find-all-combinations-that-equal-given-sum.html
You can get there a pure Excel formula solution, Solver Add-In, or VBA. Comment if you need help adapting them.
Post your Excel file if you need more help.