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:
You complete a quest simply by travelling there with the required items in your inventory (if the quest has required items, indicated by the presence of items left of an arrow under the quest). In this puzzle, gathering ingredients requires no items, brewing potions requires two particular ingredients, and selling requires two particular potions.
The items drawn around places are the reward items for the quests that can be completed there. So for instance you can brew a Potion of Energy at G, H, and J, so long as you have Silkleaf and Dryleaf. You can gather Chrylets at C, I, and K.
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. So for instance, if you already had Silkleaf in your inventory, you could both gather Dryleaf and brew a Potion of Energy in the same "turn" at either H or J.
You always start where the character Lyla is (at the bottom connected to B, C, D, and H). 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.
I will also include two more mechanics that are not relevant to this first puzzle, but I will reference this text for explanation of future puzzles:
- You can complete a quest more than once but only once per place.
- Quests are completed from top to bottom, and you cannot avoid completing quests. Consequently, completing a higher quest may prevent completing a lower quest.