Math puzzle

[iknowu99]

There are pairings and values are received one from each scale. Small scale numbers are always unique. We have sum of values that are used. We know that pairings are either summed or not. Based on sum we need the function to return which index in the array was used.

The goal is to build deciphering function to return which pairings were used to create the sum. For ex: Can you figure out which pairings were used to make the sum?

Excel
	A	B	C	D	E
1	large scale:	600	400	800	800
2	small scale:	50	51	63	64
3
4	sum:	1965
Sheet1

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[iknowu99]

The small scale has unique values while large scale can have repeats.

 

[shg]

But you still use both numbers in a given vertical pair, or neither, right?

 

[iknowu99]

But you still use both numbers in a given vertical pair, or neither, right?

Sorry. after talking it out the original question must be revised. Posting revision:

The puzzle is to figure out what's the smallest scale that can be used in order to deaggregate the sum to its parts. For example. if the index was 1,11,111,1111 and the sum appeared as 1123 then the function returns the array (1,2,4) since the numbers were used were 1, 11, 1111. but those gaps are large and would be difficult to index lots of items.

 

[shg]

This seems to be a very fluid problem. Good luck.