Puzzle Description Suppressed:Click below to view spoilers

#1: Aldege Cholette (aldege) on Jul 8, 2011 [SPOILER]

Comment Suppressed:Click below to view spoilers

ditto Aldege

i think i had to guess
i did a lot of color logic and got some of the black, all the red, and all but a couple of green and blue pixels
the black was just too hard to solve without looking several moves ahead

I got through almost all of the color with color logic. But then the look ahead was too many moves and I had to resort to trial and error for that last bit of blue. Then it solved the rest of the way okay. Too bad, because some minor adjustments could have made this solvable.

I think it is logically solveable. And a very good puzzle as well.

This puzzle was a real challenge!

tl;dr: the shortest solution I could find has 50 steps

I believe this puzzle is logically solvable with deep lookahead. Here is the way I solved it. There may be a more efficient way, and some of these steps may be unnecessary. Also, some of these steps may be taken out of order.

I use the option for “Unknown cells are grey, White cells are white.” If you use dots, please make the substitution in the logic below. The steps are numbered to help keep track of where we are in the solution.

1) There is no initial line logic, but color logic does a lot better. A good starting point is to complete these sections:
a. blue in the top left
b. red in the bottom left
c. blue in the bottom right
2) Color logic starting in the right-most column causes the following squares to be white:
a. R3 C27-29
b. R5 C27-29
c. R7 C27-29
d. R9 C27-29
e. R18 C23-29
f. R19 C23-29
g. R20 C23-29
h. R21 C27-29
i. R22 C27-29
j. R23 C27-29
k. R24 C27-29
l. R25 C26-29
m. R26 C26-29
n. R27 C26-29
3) Line logic brings the puzzle to 26% complete.
4) Color logic fills in quite a few spaces around the blue in the top left:
a. R2 C10-14 is white
b. R3 C9-14 is white
c. R4 C1-14 is white
d. C1 R5-21 is white
e. C6 R5-7 is white
f. C7 R5-7 is white
g. R8 C2-4 is white
5) More line logic is now available and brings the puzzle to 50% complete.
6) Color logic gives us these moves:
a. R30 C11-21 is white
b. R15 C23-24 is white
c. R16 C23-25 is white
d. R17 C23-26 is white
7) The following steps work in color logic because R23 has no blue clues in it
a. C16 R17-18 is blue
b. C19 R17-18 is blue
c. C20 R17-18 is blue
8) More line logic is now available and brings the puzzle to 54% complete.
9) Color logic gives us these moves:
a. R22 C2 is blue
b. C21 R17-18 is blue
c. C15 R7-9 is green
d. C14 R6-9 is green
e. R11 C9 is red
10) The red is now complete. More line logic is available. Be sure not to miss R25 C10 being white. The puzzle is now 58% complete.
11) Color logic gives us these moves:
a. R5 C12-13 are green
b. C22 R17-18 are blue
c. R20 C22 is white
d. R20 C21 is blue
e. R16 C16 is white
f. R21 C13-15 is blue
12) More line logic is now available and brings the puzzle to 61% complete.
13) Color logic gives us these moves:
a. R21 C12 is blue (else contradiction in R21 C17)
b. R19 C22 is blue (else contradiction in R19 C12)
c. R21 C20 is blue (the blue 2 clue only fits in R21 C19-21)
d. R8 C5 is white
14) A little more line logic brings the puzzle to 63%.
15) Here is where I started using moderate lookahead. First, edge logic in C2: If the green 4 clue is placed in C2 R11, a contradiction occurs in C3 R12, therefore C2 R9-11 are white.
16) Color logic on the blue 1 in R8 shows it must go in R8 C10. Line logic then makes R9 C10 white.
17) Color logic in R9 requires R9 C4 to be green. Line logic then makes R10 C4 white.
18) Color logic in R11 requires R11 C6-7 to be white. Line logic then turns R11 C4 green and R11 C8 white.
19) Color logic on the blue 1 in C3 shows that C3 R21 must be blue.
20) Line logic brings the puzzle to 67% complete as long as you catch that R10 C4 must be white.
21) Edge logic in C25, using the black 2 clue: if placed in R27-28, a contradiction is created in C23. The same contradiction occurs if placed in R26-27. Therefore, C25 R27-28 are white.
22) Edge logic in C24, using the bottommost black 2 clue: if placed in R26-29, contradictions are created in C23, therefore C24 R27-29 are white.
23) Some line logic that the hint button doesn’t find makes R21 C8 and R21 C10 white.
24) Color logic in C10 shows C10 R10-13 white, C10 R14 blue, and C10 R22-24 white. Line logic makes C10 R16 black.
25) Color logic on the blue 1 clue in C4 places it in R20 C4. Line logic finishes R20.
26) Line logic and color logic complete the green 6 clue in C4. Additional line logic brings the puzzle to 70% complete.
27) Color logic shows R16 C5 to be white.
28) The next section feels like deep lookahead to me. C3 only has a single green 1, and it can only go in 4 places. If the green one goes in:
a. R25 C3 - then a contradiction occurs in R21 C7 after the green 2 clues form a staircase. Therefore, R25 C3 is white.
b. R24 C3 - then there is a choice to make the green 2 in C4 go up or down. If it goes down, then a contradiction goes occurs in C5. If it goes up, then a contradiction occurs in R21 C6 after the green 2 clues form a staircase. Therefore, R24 C3 is white.
c. R23 C3 - then there is a choice to make the green 2 in C4 go up or down. If it goes up, then a contradiction occurs in R21 C5. If it goes down, then a contradiction occurs in R24-25 C6. Therefore, R23 C3 is white.
d. Having eliminated all 3 other options, R22 C3 must be green.
29) A little more line logic is available. Then we can use color logic on the green section in the lower left. To start, note that color logic means that R23 C4 must be green. Color and line logic show the green 2 clue staircase must go down and right, and ends in R27 C8.
30) After a bit of line logic, the puzzle reaches 73% complete.
31) Color logic forces the green 2 clue in R29 to be in C9-10, therefore R29 C9-10 must be green. More color logic shows R30 C10 to be green.
32) Line logic shows R30 C9 and C10 R26-28 to be white.
33) Next might be deep lookahead: Edge logic for the top black 2 in C24, if placed in R13-14, causes a contradiction in R15C21, therefore C24 R13-14 must be white. A little line logic follows and brings the puzzle to 76% complete.
34) Line logic not found by the hint button shows R25 C21 and R27 C21 are white.
35) A bunch of line logic now follows, and brings the puzzle to 83% complete.
36) Line logic not found by the hint button shows R14 C9 and R16 C9 to be white.
37) Color logic shows R22 C5 to be white. Then R21 C5 must be white.
38) Now for some internal edge logic. If the black 4 clue in C14 goes in R15-18, a contradiction appears in R16 C13, therefore R18 C14 must be white.
39) Now for some color logic combined with two-way logic. Examine R17. The blue 1 clue can only go in R17 C6 or R17 C7. No matter which location the blue 1 clue is placed, R17 C8 must be black.
40) Time for some advanced color logic in R18. There is a single blue 1 clue in R18, and no other remaining blue. That blue clue can go in C5-8. There is only a single clue unplaced to the right of that blue 1 clue, which is a black 2 clue. Now for the trick: If R18 C9 is black, that square must be part of the black 2 clue, since the blue 1 clue cannot go to the right of it. Therefore, if R18 C9 is black, R18 C8 must also be black, but this causes a contradiction. Therefore R18 C9 must be white.
41) Line logic now makes C9 R27-28 black.
42) Edge logic in C11: When placing the black 2 clue, if placed in C11 R27-29, a contradiction occurs in C12. Therefore C11 R28-29 must be white. A bit of line logic follows, bringing the puzzle to 85% complete.
43) Two way logic: Whether or not R22 C13 is black or white, R25 C12 is white.
44) More line logic follows. R23 C8 is white, but doesn’t show on the hint button. After this, more line logic moves the puzzle to 88% complete.
45) Color logic in R17: R17 C8 is black, and must be part of the left black 2 clue. Either R17 C7 or R17 C9 must be black. If R17 C7 is black, it causes a contradiction, therefore R17 C9 must be black. A tiny bit more line logic follows.
46) Color logic in C7: The square R15 C7 must be either the bottom black 1 clue or the top black 2 clue in C7. Because the blue 1 clue in C7 must be in R17-19, the black square R15 C7 must be the top black 2 clue. Therefore, R14 C7 must be black.
47) A bunch of line logic follows, which finally completes all the green squares! The puzzle has reached 94% complete.
48) Color logic in R17: The blue 1 clue can only go in R17 C7.
49) Internal edge logic in R19: If the black 5 clue in R19 is placed in R19 C11-12, a contradiction occurs in R18 C11, therefore R19 C12 must be white.
50) Line logic first completes the blue, then solves the puzzle.

Happy Solving!

Show: Spoilers

Goto next topic

You must register and log in to be able to participate in this discussion.