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Background
You'll receive this quest from Timmon in Harviken on Faroe in
The Skellige Isles Southeast (#1).
Walkthrough
Timmon will tell you that his brothers Mikkel and Ulf sailed to Hindarsfjall to pick up his betrothed Agda, but that none of them have been seen since. So he'll ask you to keep an eye out for them while he continues to plan for the upcoming wedding.
To begin your search, you should make your way to the northeastern coast of Faroe (#2). There you'll spot two sirens feeding on Agda's corpse. After defeating the sirens, when you examine Agda, you'll see that she drowned.
To determine what happened, you'll need to use the
Magic Lamp, which you should have gained during the Velen quest
An Invitation from Keira Metz. When you shine the lamp on Agda's corpse, you'll have a vision of Timmon's brothers. They'll mention three things of interest: that Adga drowned during a storm as they were sailing back from Hindarsfjall, that Agda's dowry went down with the ship, and that the only way for them to restore their family honor is to commit suicide.
To find the brothers, you'll need to turn on your witcher senses and follow their footprints to the east. The footprints will lead you to the tree where the brothers killed themselves (#3). When you examine the two corpses, you'll find a Chest Key and a Letter from Agda's Father to Timmon.
Before returning to Timmon, you should locate Agda's dowry. If you return to Agda's corpse, then you'll see a ship's mast in the water to the northeast (#4). When you swim out to it, you'll discover a locked chest on the main deck of the ship. The Chest Key will open it, and inside you'll find a
Gold Diamond Necklace.
When you return to Timmon (#1), you'll have to make a decision. You can either give him the necklace (worth 600 crowns) or you can keep it for yourself. Either way, you'll earn 75 xp for completing the quest.
1 - Harviken
2 - Agda
3 - Brothers
4 - Ship