First fill in the trivial german whispers, then do the nabners. Clues: - Apart from very long GW lines (11 long), they start low-high. - The 2nd cell cannot be deduced. If AB=A+B+tail, then A0=A+tail - Thence, A*9=tail - If you're pushed to maximise, taking 1 from the 9 in a -4-9-4- takes 3 off the total as it must become -3-9-3-. Similar upwards in -1-6-1- if you're trying to minimise. A length-5 can only be 1-?-"9-from-3", therefore is -1-7-1 A length-7 can only be 2-?-"18-from-5" or 3-?-"27-from-5", but you can't make the former. The tail of 3-[89]-2-[89]-[34]-[89]-[34] sums to 24..28, so maximising with 1 slack forces 9s, and leaves a [34] pair. Fill in the 5-nabner 7-9-5-1-3. Finish the length-7 GW and box 3. Pencil box 2. A length-8 can only be 3-?-"27-from-6" or 4-?-"36-from-6". The tail of [34]-[89]-[234]-[89]-[13]-[78]-2-7 sums to 27..33, so minimise it. A length-6 can only be 2-?-"18-from-4". So it's 2-[789]-2-8-1-7. Pencil box 6. Pencil box 1. The renban in it must have 1 low value, that's [23] in R2C2. r2c1 can only be [248], so the renban can't be [2468], therefore needs 9 in r3c2. Do trivial sudoku: 5 goes in r4c1, and youi can complete boxes 4, 2, 1, 6, and 5. The final renban should be no slacker than [17]-[49]-[57]-[36], and a 6 at the end kills the [57], so is a 3, making the [49] a 9. If either of the potential 7s is a 7, then they are both forced to be, so neither is. Bosch! Proof of uniqueness: https://sigh.github.io/Interactive-Sudoku-Solver/?q=.Whisper%7E5%7ER1C6%7ER1C7%7ER1C8%7ER2C9%7ER3C9%7ER4C8%7ER4C7.Whisper%7E5%7ER5C1%7ER5C2%7ER6C3%7ER6C4%7ER5C5%7ER4C5%7ER3C6%7ER3C7.Whisper%7E5%7ER4C2%7ER4C3%7ER3C4%7ER2C4%7ER1C3.Whisper%7E5%7ER7C5%7ER7C6%7ER8C7%7ER8C8%7ER7C9%7ER6C9.Or.And.%7ER1C6_2.Sum%7E18%7ER1C8%7ER2C9%7ER3C9%7ER4C8%7ER4C7.End.And.%7ER1C6_3.Sum%7E27%7ER1C8%7ER2C9%7ER3C9%7ER4C8%7ER4C7.End.End.Or.And.%7ER5C1_3.Sum%7E27%7ER6C3%7ER6C4%7ER5C5%7ER4C5%7ER3C6%7ER3C7.End.And.%7ER5C1_4.Sum%7E36%7ER6C3%7ER6C4%7ER5C5%7ER4C5%7ER3C6%7ER3C7.End.End.Sum%7E9%7ER3C4%7ER2C4%7ER1C3.Sum%7E18%7ER8C7%7ER8C8%7ER7C9%7ER6C9.%7ER4C2_1%7ER7C5_2.BinaryX%7E8H-xf8H-xf8H-B%7E_nabner%7ER1C1%7ER2C2%7ER3C2%7ER4C1%7E%7ER8C9%7ER9C8%7ER9C7%7ER8C6%7E%7ER3C8%7ER2C7%7ER2C6%7ER1C5%7ER2C4