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This is a puzzle from the Expert section of my game Fetching Alchemist, visually modified for presentation here. It is a variant of the Travelling Salesman problem where you are trying to complete a set of quests.

The red numbers indicate the distance of each road. You need to find the shortest path that allows you to complete all the quests. Present your answer in the form "ABCDE", where the letters are the places you visit on the path.

Shortest path distance for this puzzle:

82

You complete a quest simply by travelling there with the required items in your inventory, which are consumed upon completing the quest (if the quest has required items, indicated by the presence of items left of an arrow under the quest).

The items drawn around places are the reward items for the quests that can be completed there.

You can complete a quest more than once but only once per place.

You can complete more than one quest in the same place. When completing more than one quest in the same place, quests are completed automatically from top to bottom, and you cannot avoid completing quests. Consequently, completing a higher quest may prevent completing a lower quest.

If you would obtain an item from completing a quest, you can use it to complete a quest in the same place without travelling again.

You always start where the character is. You cannot return to the starting place once you have left. This is because, in the game, returning to the start is how you reset the puzzle.

If you are still unsure how to play, have a look at the first solved puzzle.

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Completed in

82, as desired, via DBCIFJ:
Travel to B via D, and pick up Rainbow Rattles and a Blood Vial.
Go to C, where you pick Stardrops and immediately combine them with the Rattles to form the Potion of Power. Also get Sunbells.
Go to I, where you get Dusk Puffs in preparation for the Autumn Reagent.
Stop at F to gather more Stardrops and immediately brew the Potion of Nature.
Finally, visit J to brew the Autumn Reagent, and immediately sell all three of your potions!

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  • $\begingroup$ Yes! Good job! . $\endgroup$ Apr 18 at 1:01
  • $\begingroup$ To help me understand the mechanism more, you can already brew Autumn Reagent in F right? $\endgroup$
    – justhalf
    Apr 18 at 2:50
  • $\begingroup$ @justhalf You may be mistaking the Blood Vial at F for an Autumn Reagent? They are both red but the Autumn Reagent is fatter. Alternatively you may be assuming that you can brew anywhere. All quests in this puzzle have certain places where they can be completed, and because there is no Autumn Reagent at F, it can't be completed there. $\endgroup$ Apr 18 at 3:16
  • $\begingroup$ I mean, we already have the Dusk Puffs and at F we can get the Blood Vial to brew Autumn Reagent, right? $\endgroup$
    – justhalf
    Apr 18 at 4:03
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    $\begingroup$ Ah, I got it. So the icons mean the recipe to get that item (if it's crafted) is there, not that they are selling the item. Got it. A bit confused because I thought once you have the components of the recipe, you will automatically brew it. $\endgroup$
    – justhalf
    Apr 18 at 4:05

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