Sujiko 1

I've just published this puzzle on the assassin site, however in the creating my next one the following question came to mind:

If the 25 sums give a feasible solution is it automatically unique in all cases? i.e. necessary equals sufficient.

Whether it is solvable without heavy number crunching is a separate matter - although even then the analysis is only of spreadsheet level.

I am currently attempting to create a counter example.

Puzzle: Sujiko 1

I've been doing these in the (UK) Sunday Telegraph - with difficulty. Hence I thought to create them so as to understand the solution methodology better.

The clues are the sum of the adjacent four squares.

The numbers 1-9 cannot repeat in the blue nonets.

Numbers can repeat in rows and columns.

Numbers can repeat in clue sums.

Given the central clue this puzzle is not that hard, hence I have left out a few sums. I am never sure whether to do this as leaving out clues makes the solution path clearer, if more difficult.