Overview: ========= - find enough 5's, 4/6's, 1/9's and colour hi/lo - push german whisper implications as far as you can - do some sudoku - put the 3 in the corner - finish up Finding 5s, 4/6s, 1/9s ---------------------- Row 1, 3, column 9 and box 6 reveal their 5s immediately. 3 of those are on raisins, so place [46]s and [19]s. Box 9 with two [46] lets us start colouring for high/low. Arbitrarily, I'll make the r9c9 [19] pink, and its [46] green. The green [19] in row 9 must be in box 7, as box 8 already has a green [19]. The 5 in row 9 must be on a raisin, with a [46], so must connect to the green [19], therefore is in the corner, and its [46] is pink. => the green [46] in row 9 in r9c6, connected to a green [37] and a blue [28] => the green [28] is in r9c8, connecting to a pink [37]. => the green [28] in box 8 is r7c4 => the [46] in r1c6 is pink, with green-pink-green to its right. Column 9 has 2 greens, but rows 2,3, and 5 are of the same colour, so are pink. => the pink [46] in column 9 is on the raisin with a pink [37] => r5c9 is pink [28] as there are two pink [3478]s in the column, it's flanked by green [1289]s. Push German Whisper implicaitons -------------------------------- Row 1's green [46] is in r1c1 or r1c4, and between those two positions must be the pink [18]. => r1c8 is pink [2378], however, the pink [3467] pair in the box preculdes [37] from r1c8, it's [28] => r1c9 is a green [2378] If that line ended -p[28]-g[28], then you'd need g[37] to be next to p[37] on the other line in row 1 => r1c9 is a green [37] => row 1 begins forward or backwards with g[46]-p[19]-g[28]-p[37]. [[[ Intermission -------------- At this point, knowing there's a unique solution lets us putgreen [46] in r1c1, as if it was pink [37] you'd be guaranteed a 3 in one of the two corners, but have *no* rules in the whole puzzle that permit you to decide between high and low. Replacing N with 10-N in all cells would leave an equally valid solution - only the 3 in the corner splits the parity. So we could now place it in r1c9, and map green to low, and blue to high were we willing to assuming uniqueness. But we won't. ]]] green [46] is needed in row 3, naive candidates include [r3c1, r3c4, r3c6, and r3c7 It can't be r3c6, because you can't put a pink [19] in r3c7, as that would put 2 pink [28]s in box 6. It can't be in r3c1 because pink [19] is already in box 1 It can't be in r3c5 as the green [37] it would share the raisin with clashes with r9c5. => r3c7 is green [46], flanked by 2 pink [19]s Row 3 now has 2 placed pinks, and columns 2,4, and 5 are the same colour so must be green green [28] in row 3 can't be in r2c2 as that would break the raisin, nor in r3c4 due to r7c4, so is in r3c5 pink [37] cannot be between two green [1379]s on a GW, so r3c3 is pink [28]. r3c1 is pink [3467], so can't abut a [37], so r3c2 is green [19] and r3c4 is green [37] Do some sudoku -------------- pink [28] in column 7 can only be r8c7 green [28] in column 7 can only be r2c7 green [37] in column 7 can only be r5c7 pink [19] in column 8 can only be r2c8 r7c8 and r8c8 are green [37] and green [19]. Row 7 has three placed greens, with the fourth (the g[46]) being in r7c2 or r7c3 => r7c1 is pink => r6c1 and r8c1 are green, and r5c1 and r4c1 are blue => r2c1 is green [37] and r1c1 is green [46] => row 1 begins g[46]-p[19]-g[28]-p[37] Put the 3 in the corner ----------------------- There's one one place for it, r1c9, and it makes green low, pink high. Finish up --------- In column 1, if r3c1 is 6, then the raisin contains an 8, and if it's 7, then the raisin contains an 8. => r7c1 isn't 8 => The 8 in row 7 is in r7c2 => r7c3 is 4, and r5c3 on the raisin must be 3 => r8c2 is box 1's 3. The [79] pair on the german whisper forces r3c1 to be 6, and r4c1 to be 8. The and 2 can be placed in column 1 Column 9 resolves fully The innermost german whisper, having a 3 at one end, must continue with a 9 and a 1. => r5c8 is green/low, and thus 4 Box 1 completes, [79] pairs resolve, and it's all just simple speedrunning at this point. Proof of uniqueness ------------------- https://sigh.github.io/Interactive-Sudoku-Solver/?q=.Whisper%7E5%7ER1C1%7ER1C2%7ER1C3%7ER1C4.Whisper%7E5%7ER1C6%7ER1C7%7ER1C8%7ER1C9.Whisper%7E5%7ER3C9%7ER4C9%7ER5C9%7ER6C9.Whisper%7E5%7ER8C9%7ER9C9%7ER9C8%7ER9C7.Whisper%7E5%7ER9C5%7ER9C4%7ER9C3%7ER9C2.Whisper%7E5%7ER8C1%7ER7C1%7ER6C1%7ER5C1.Whisper%7E5%7ER3C1%7ER3C2%7ER3C3%7ER3C4.Whisper%7E5%7ER3C6%7ER3C7%7ER4C7%7ER5C7.Whisper%7E5%7ER7C7%7ER7C6%7ER7C5%7ER7C4.Whisper%7E5%7ER6C3%7ER5C3%7ER5C4%7ER5C5.WhiteDot%7ER2C9%7ER3C9.WhiteDot%7ER1C5%7ER1C6.WhiteDot%7ER7C9%7ER8C9.WhiteDot%7ER9C6%7ER9C5.WhiteDot%7ER5C1%7ER4C1.WhiteDot%7ER3C5%7ER3C4.WhiteDot%7ER6C7%7ER7C7.WhiteDot%7ER7C3%7ER6C3.WhiteDot%7ER9C2%7ER9C1.%7ER1C9_3 Note that that has placed the 3 in the corner, without that, it's parity-ambiguous: https://sigh.github.io/Interactive-Sudoku-Solver/?q=.Whisper%7E5%7ER1C1%7ER1C2%7ER1C3%7ER1C4.Whisper%7E5%7ER1C6%7ER1C7%7ER1C8%7ER1C9.Whisper%7E5%7ER3C9%7ER4C9%7ER5C9%7ER6C9.Whisper%7E5%7ER8C9%7ER9C9%7ER9C8%7ER9C7.Whisper%7E5%7ER9C5%7ER9C4%7ER9C3%7ER9C2.Whisper%7E5%7ER8C1%7ER7C1%7ER6C1%7ER5C1.Whisper%7E5%7ER3C1%7ER3C2%7ER3C3%7ER3C4.Whisper%7E5%7ER3C6%7ER3C7%7ER4C7%7ER5C7.Whisper%7E5%7ER7C7%7ER7C6%7ER7C5%7ER7C4.Whisper%7E5%7ER6C3%7ER5C3%7ER5C4%7ER5C5.WhiteDot%7ER2C9%7ER3C9.WhiteDot%7ER1C5%7ER1C6.WhiteDot%7ER7C9%7ER8C9.WhiteDot%7ER9C6%7ER9C5.WhiteDot%7ER5C1%7ER4C1.WhiteDot%7ER3C5%7ER3C4.WhiteDot%7ER6C7%7ER7C7.WhiteDot%7ER7C3%7ER6C3.WhiteDot%7ER9C2%7ER9C1