# Sudoku Logic From Another Planet

This is the brutally hard Tatooine Sunset Sudoku puzzle by Philip Newman ... except the Noble Happy Star has goofed! Two of the digits have been swapped and there are multiple solutions. Fortunately, you are not required to solve the whole puzzle. All you need is six measly digits – or more precisely – their sum.

Let the sum of the six gray cells be X. Your task is to determine all possible values of X.

Acknowledgements: I wish to thank Simon Anthony and Mark Goodliffe for uploading the original Tatooine Sunset puzzle and solution. Thanks also to Tom Collyer and Sam Cappleman-Lynes for further discussion of relevant solving techniques.

EDIT: In response to Bass's comment: the original Tatooine Sunset puzzle has r3c2=8, r4c8=3 and this has a unique solution.

• Puzzles posted here should be self-contained; if the link to the remote source ever stops working, we don't want the puzzle to become meaningless. – Bass Oct 20 '20 at 6:52
• To clear any confusioni: normal Sudoku rules apply and the left diagram is meant to be a hint for my intended solution path. I've tagged the problem as lateral thinking because I have not seen anything resembling my intended logic elsewhere before (not sure if that tag is appropriate though). – happystar Oct 20 '20 at 7:26
• what are the rules of this sunset puzzle? I quick google search did not turn up anything useful – daw Oct 20 '20 at 8:15
• @daw It's just a standard sudoku (you don't need the colors outside the sudoku), except that it has multiple solutions according to OP. – Bubbler Oct 20 '20 at 8:34
• @Bubbler seems not to be the case given the answer below :( – daw Oct 20 '20 at 15:47

25

Using the provided buckets it's actually exhilaratingly simple.

Observing that the green to green and the blue to blue buckets are both completely full and have apart from 8 no entries in common, we can immediately infer the green to red, ref to green blue to red and red to blue buckets almost completely.

How the buckets work:

Buckets pool things. A row of buckets contains three ordinary rows and similar for columns. Therefore a row of buckets must contain 3 of each kind. Because of the pecularities of this specific puzzle we can infer almost everything we need. For example, one 3 in g2g means max 2 3s in g2b, means as no 3s in b2b at least 1 3 in r2b and we see that r2b must replicate almost the entire g2g.

The last piece of information comes from observing that red to red has one row completely filled. Therefore everything not in that row can occur only 2x max. Therefore the missing bits in r2g r2b (same for g2r b2r) must be a 1 and an 8. The rest is counting,

• Well done. Note that in the original Tatooine Sunset puzzle (swap r3c2 with r8c4) this analysis yields the digit r1c7=8. With some more effort, one can prove r6c7 != 1 and this resolves all the grey cells. – happystar Oct 21 '20 at 8:56