Finding Possible Matches to a Solution

The key to begin to solve the problem is to recognize the type of problem.

This is the classic subset sum problem which can be handled by generating all possible combinations without repetition and then selecting only those rows which = target sum.

SubsetSumλ = 

LAMBDA(
    integers,   //array of numbers
    target_sum, //return rows which = this target
LET(
//Total numbers
    k, COUNT(integers),
//Total combinations
    C, SUM(COMBIN(k, SEQUENCE(k))),
//Generate bin array using BITRSHIFT to avoid limits of DEC2BIN
    bin, MOD(BITRSHIFT(SEQUENCE(C), SEQUENCE(, k, k - 1, -1)),2),
//Swap binary for integers
    M, bin * TOROW(integers),
//Check which rows = target sum
    keep, BYROW(M, SUM) = target_sum,
//Deliver results
    deliver, FILTER(M, keep, "None"),
    deliver));