sum is large enough that there are no solutions with less terms available.
Missed that part.
Never mind. - Emila Latella
Not quite. You've come up with a way to find numbers that have exactly one six-term solution. The problem was to come up with numbers that have exactly one solution and that one solution has six terms (or as many terms as possible while still only having one solution). This analysis can find you good candidates, but you'd have to vet them by demonstrating that they also have no solutions involving fewer terms.