Puzzle Description:

(This puzzle was recovered from the 2016 database crash. Description not available.)

#1: Wombat (wombatilim) on Mar 11, 2023 [HINT]       classify

Initial line & color logic gets 57% complete. Green is finished, and we have definite areas where the remaining red (R41-50 C11-28) and black (R41-50 C44-52) need to go.

C18: EL marks R4-12 and R37-38 white.
C19: EL marks R4-12 white.

R8: If the 3 is in C20-22, it will need to use the 2s in C21-22. Whichever way these go, it will make C20 invalid. Therefore R8C20-22 is white.

R4: There is no way to place the 1 in C20-22 that doesn't create a contradiction in R3, so these squares are white.

Deep lookahead R12: If the blue in C40 is part of the 10, it puts the 1 into C29, which completely places the 4 into R9-12C29. This means the blue in R10C40 must be part of the last 2 in that row. R12 would need to reach both C37 and C45. In each of these columns, the only available clue that does not contradict in R10 is the 1, which means the blue in R11C40 could not be part of the 10 in that row, and R11 C49-57 would need to be blue. Conversely, if the blue in R12C40 is *not* part of the 10, it puts blues into R12 C49-57, which *also* would put blues into R11 C49-57. Therefore, R11 C49-57 are definitely blue. Finally some line and color logic.

C22: IEL (v. C20) marks R32-38 white. Line & color logic.
R21: If the 5 is *not* in C18-22, it creates a contradiction in R29. Line & color logic.
C18: EL marks R34-36 white. Line & color logic.
C36: EL puts the blue 5 in R21-25. Line & color logic.

Summing: R51-60 has a total of 128 blues to place. The blues that we know *must* be in those rows (C22-35, the blues below green in C36-41, and the blues below black in C44-52) total 106, leaving 22 unaccounted for. C42 has 7 possible and C43 has 8 possible, which leaves at least 8 more needed in C53-57. Just using C55-57 still only gives us 6, so we absolutely must use at least one of the 4s in C53-54. If we are using the 4 in C54, we would have to use the 4 in C53 as well anyway, so we know for certain the 4 in C53 has to be positioned in R51-60.
TL;DR: R14-19, R21-24, and R28-30 in C53 are white. Line & color logic.

C54: EL can now mark R14-19, R28-32, and R34-38 white.
C55: EL marks R14-19, R28-32, and R34-38 white. Line & color logic.
C56: EL marks R14-19 white. Line & color logic.

C45: If the blue in R25 is the 1, it makes C44 invalid. Therefore it is part of either the 3 or the 5, and R23-24 C45 are blue. Line & color logic.

Deep lookahead C40: If the blues in R23-25 are the 3, it marks R28-30 C40 white, which also marks R33 C36-39 white. That leaves 2 possible positions for the 5 in C39, both of which would make C38 invalid. Therefore R21-22 C40 are blue. Small amount of LL.

Deep lookahead C41: If the blues in 24-25 are part of a 2, there is nowhere to put the 5 in that column that still leaves room for both 3s in C37. Therefore R23C41 is blue. Minimal LL.

I need to break here for now. I'm currently at 74%. Right now I'm leaning towards "requires guessing" but I also don't think I've exhausted all the lookahead yet.

Picking up where I left off:

Deep lookahead summing: R28-38 have a total of 41 blue squares to place. We can count 27 total blues that we know for certain go in these rows in C36-46, leaving 14 blues for C41-43 and C45-46. The options are as follows:
- C41: 0 or 3
- C42: 0 or 3 or 7
- C43: 0 or 3 or 7
- C45: 0 or 3
- C46: 0 or 2
If we take one of the 7s, the only way to add up to 14 is by using the other 7, and using 0 from the other columns in question. This would make C41, C45, and C46 all white in these rows. The 4s in C42-43 would both have to place blue in R35-37, which would use up the 3 in C44. This does not leave enough room for the 3s in C42-43. Using the 7s therefore makes this section invalid, and the remaining 3s and 2 add up to 14 exactly.

This conclusion doesn't help us solve R28-38 right away, but it does help us with C41 and C45-46. R21-22 in C41 and C45 are blue, and R4-12, R14-19, and R21-22 in C46 are white. LL.

We now have 5 distinct sections remaining and we can tell which clues go in which section:
- R41-50 C11-28 contains all remaining red clues.
- R41-50 C44-52 contains all remaining black clues.
- R4-19 C36-45 contains the blue clues above the ones used in R21-25, and there is no ambiguity about which ones those are.
- R51-60 C22-57 contains the lowest blue clue in each of those columns and no others.
- R28-38 C36-46 contains the remaining blue clues.

Stuck here again, currently at 75%, but I haven't given up completely yet.

I had no problem solving the red and black but the blue was tricky

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