I’m enjoying Towers by Simon Tatham (guidelines are within the hyperlink). This sport shares some resolution logic to Sudoku.

I not too long ago moved to the final urged degree of issue, 6×6 Unreasonable, however I apparenly miss a software in my belt to unravel that degree of issue as a result of everytime I strive one, I am unable to end it with out backtracking.

I need to remedy the next puzzle (playable right here), however with out utilizing backtracking (that’s guessing a sq., then coming again to the earlier state if I discover any battle). Is there an answer with out backtracking or is backtracking the final transfer I needed to study to grasp this sport?

               4   2
  +---+---+---+---+---+---+
  |   |   |   | 2 |   |   | 3
  +---+---+---+---+---+---+
2 |   |   |   |   |   |   |
  +---+---+---+---+---+---+
2 |   |   |   |   |   |   | 2
  +---+---+---+---+---+---+
2 |   |   |   |   |   |   | 1
  +---+---+---+---+---+---+
  |   |   |   |   |   |   |
  +---+---+---+---+---+---+
  | 2 |   |   |   |   |   |
  +---+---+---+---+---+---+
    4       1       3   2

And right here is my present standing:

My present save file (save as any file, however add it on the sport web page):

SAVEFILE:41:Simon Tatham's Portable Puzzle Collection
VERSION :1:1
GAME    :6:Towers
PARAMS  :3:6du
CPARAMS :3:6du
SEED    :15:371209209321014
DESC    :41:///4/2//4//1//3/2//2/2/2///3//2/1//,c2z2e
AUXINFO :74:e55bd588ce7f80ffc06c9b2cdb35783c4b0b4022ca6a0f00b6a8156e7761a0de3f273a075b
NSTATES :3:214
STATEPOS:3:213
MOVE    :1:M
MOVE    :6:R2,5,6
MOVE    :6:R5,3,6
MOVE    :6:R0,3,5
MOVE    :5:D-1,3
MOVE    :4:D6,3
MOVE    :4:D2,6
MOVE    :6:P0,4,1
MOVE    :6:P0,4,2
MOVE    :6:P0,4,6
MOVE    :6:P0,4,5
MOVE    :6:P0,0,2
MOVE    :6:P0,1,2
MOVE    :6:P0,2,2
MOVE    :6:P1,5,2
MOVE    :6:P3,5,2
MOVE    :6:P4,5,2
MOVE    :6:P5,5,2
MOVE    :6:P3,4,2
MOVE    :6:P3,3,2
MOVE    :6:P3,2,2
MOVE    :6:P3,1,2
MOVE    :6:P5,0,2
MOVE    :6:P4,0,2
MOVE    :6:P2,0,2
MOVE    :6:P1,0,2
MOVE    :6:P0,0,2
MOVE    :6:P0,0,2
MOVE    :6:P3,1,5
MOVE    :6:P3,1,6
MOVE    :6:P3,2,6
MOVE    :6:P2,0,6
MOVE    :6:P2,1,6
MOVE    :6:P2,2,6
MOVE    :6:P2,3,6
MOVE    :6:P2,4,6
MOVE    :6:P1,5,6
MOVE    :6:P3,5,6
MOVE    :6:P4,5,6
MOVE    :6:P5,5,6
MOVE    :6:P4,3,6
MOVE    :6:P3,3,6
MOVE    :6:P2,3,6
MOVE    :6:P1,3,6
MOVE    :6:P2,3,6
MOVE    :6:P5,2,6
MOVE    :6:P5,1,6
MOVE    :6:P5,0,6
MOVE    :6:P5,0,5
MOVE    :6:P4,0,6
MOVE    :6:P0,1,6
MOVE    :6:P0,2,6
MOVE    :6:R0,0,6
MOVE    :6:P1,0,6
MOVE    :6:P5,5,1
MOVE    :6:P5,4,6
MOVE    :6:P5,4,5
MOVE    :6:P4,4,6
MOVE    :6:P4,2,5
MOVE    :6:P3,2,5
MOVE    :6:P2,2,5
MOVE    :6:P1,2,5
MOVE    :6:P0,1,5
MOVE    :6:P0,2,5
MOVE    :6:P1,3,5
MOVE    :6:P2,3,5
MOVE    :6:P3,3,5
MOVE    :6:P4,3,5
MOVE    :6:R3,4,6
MOVE    :6:R3,5,5
MOVE    :6:P1,4,6
MOVE    :6:P1,5,5
MOVE    :6:P4,5,5
MOVE    :6:P5,5,5
MOVE    :6:P5,4,5
MOVE    :6:P5,4,5
MOVE    :6:P5,4,4
MOVE    :6:P3,1,4
RESTART :41:///4/2//4//1//3/2//2/2/2///3//2/1//,c2z2e
MOVE    :6:R2,5,5
MOVE    :6:R2,5,6
MOVE    :6:R5,3,0
MOVE    :6:R5,3,6
MOVE    :1:M
MOVE    :6:P0,2,6
MOVE    :6:P5,2,6
MOVE    :6:P1,2,5
MOVE    :6:P2,2,5
MOVE    :6:P3,2,5
MOVE    :6:P4,2,5
MOVE    :6:P0,1,6
MOVE    :6:P0,3,6
MOVE    :6:P1,3,6
MOVE    :6:P2,3,6
MOVE    :6:P3,3,6
MOVE    :6:P4,3,6
MOVE    :6:P5,0,6
MOVE    :6:P5,1,6
MOVE    :6:P5,2,6
MOVE    :6:P5,2,6
MOVE    :6:P5,4,6
MOVE    :6:P5,5,6
MOVE    :6:P5,4,5
MOVE    :6:P5,5,1
MOVE    :6:P5,0,1
MOVE    :6:P5,0,2
MOVE    :6:P5,0,5
MOVE    :6:P4,0,6
MOVE    :6:P4,0,2
MOVE    :6:P3,1,2
MOVE    :6:P3,2,2
MOVE    :6:P3,3,2
MOVE    :6:P3,4,2
MOVE    :6:P3,5,2
MOVE    :6:P2,0,2
MOVE    :6:P1,0,2
MOVE    :6:P1,1,2
MOVE    :6:P1,1,2
MOVE    :6:P0,0,2
MOVE    :6:P0,1,2
MOVE    :6:P0,2,2
MOVE    :6:P0,3,2
MOVE    :6:P0,4,2
MOVE    :6:P1,5,2
MOVE    :6:P3,5,2
MOVE    :6:P4,5,2
MOVE    :6:P3,5,2
MOVE    :6:P5,5,2
MOVE    :6:P1,5,6
MOVE    :6:P3,5,6
MOVE    :6:P4,5,6
MOVE    :6:P4,5,5
MOVE    :6:P4,4,6
MOVE    :6:P0,4,5
MOVE    :6:P0,4,6
MOVE    :6:R0,0,6
MOVE    :6:P1,0,6
MOVE    :6:P2,0,6
MOVE    :4:D6,3
MOVE    :4:D2,6
MOVE    :6:P0,3,1
MOVE    :6:P2,1,6
MOVE    :6:P2,2,6
MOVE    :6:P2,3,6
MOVE    :6:P2,3,6
MOVE    :6:P2,4,6
MOVE    :6:P3,1,5
MOVE    :6:P3,1,6
MOVE    :6:P3,2,6
MOVE    :6:R3,4,6
MOVE    :6:P1,4,6
MOVE    :6:P5,0,1
MOVE    :6:R0,3,5
MOVE    :6:P0,1,5
MOVE    :6:P0,2,5
MOVE    :6:P1,3,5
MOVE    :6:P2,3,5
MOVE    :6:P3,3,5
MOVE    :6:P4,3,5
MOVE    :6:R3,5,5
MOVE    :6:P1,5,5
MOVE    :6:P5,5,5
MOVE    :6:P3,1,4
MOVE    :6:P3,2,3
MOVE    :5:D-1,3
MOVE    :6:R5,2,5
MOVE    :4:D6,2
MOVE    :6:P5,1,5
MOVE    :6:P0,4,1
MOVE    :6:P5,4,4
MOVE    :4:D0,6
MOVE    :6:P3,2,3
MOVE    :6:P3,3,3
MOVE    :5:D3,-1
MOVE    :6:P1,1,5
MOVE    :6:P1,1,4
MOVE    :6:P1,2,4
MOVE    :6:P4,1,5
MOVE    :6:R2,1,5
MOVE    :6:P2,0,5
MOVE    :6:P2,4,5
MOVE    :6:R1,1,6
MOVE    :6:P1,2,6
MOVE    :6:P4,1,6
MOVE    :6:R4,2,6
MOVE    :6:P4,0,1
MOVE    :6:R0,2,4
MOVE    :6:P0,1,4
MOVE    :6:P0,4,4
MOVE    :6:R0,4,3
MOVE    :6:R0,1,1
MOVE    :6:P2,2,4
MOVE    :6:P3,2,4
MOVE    :6:P1,4,3
MOVE    :6:P2,4,3
MOVE    :6:P4,4,3
MOVE    :6:P5,4,3
MOVE    :6:R3,3,4
MOVE    :6:P2,3,4
MOVE    :6:P1,3,4
MOVE    :6:P4,3,4
MOVE    :5:D-1,2
MOVE    :5:D-1,1
MOVE    :6:P3,1,1
MOVE    :6:P4,1,1
MOVE    :6:P5,1,1
MOVE    :6:R3,1,3
MOVE    :6:R3,2,1
MOVE    :6:P2,2,1
MOVE    :6:P1,2,1
MOVE    :6:P4,1,3
MOVE    :6:P5,1,3
MOVE    :6:P4,4,1