Re: harder 5x5 twin puzzles

pnm wrote:

... I'll raise the stakes a bit then ...

A slightly harder example (the left puzzle should not be solvable

on its own, for example):

...

Yes, because the left puzzle by itself can have these two solutions (so not a unique solution):

21435

52314

34251

45123

13542

and

24153

32415

53241

15324

41532

but the right puzzle is solvable again alone (

**without the cooperation of the left side**): c5 = 5 (addition rule, two leftmost columns) >>> c1 = 1, d1 = 5. Now, since: 9 + b2 + 6 + (15 - c3) = 30 (two upmost rows) >>> b2 = c3 and this quickly permits to eliminate a4 = 2, a5 = 1, b5 = 3 ... driving to the unique a4 = 1, a5 = 4, b5 = 1 >>> b1 = 4, a1 = 2 (e1 = 3), a2 = 3 >>> b2 = 2 = c3 ... finding inmediately the rest of the unique solution.