Your girlfriend's half-brother and his friend have gotten themselves lost in a storage room in some abandoned building. Luckily, you were nearby enough to break in to help them. As you reach the storage room in question, you notice a small map scribbled on the wall, which looks like this:

Maze Map

Unfortunately, it seems the two of them didn't see the map, as they can only tell you that they're sitting at two different T-junctions

Just then, you notice a crate full of mutant pumpkin shells and have an idea. Instead of going in and getting lost, you could use your telekinetic powers to move these shells. While you cannot feel things through your power, you can move them on a path through the maze and return them to see if they struck anyone. The friend is indestructible and cannot feel pain and the brother once threatened to get your landlady arrested, hence you don't care how many times they are struck. However, conserving the shells is important as you do not know how many there are

You can move a shell on a path through the room that starts and ends at the door (where you are). The walls appear to be too narrow to maneuver the shells around, so if they pass by either individual it will hit them. You can't really tell how many times a shell hit someone. Due to this, you also cannot reuse shells. What is the minimum number of shells required to locate the two lost individuals

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    $\begingroup$ Can you reuse a shell multiples times ? Do you need to send all shells at once ? $\endgroup$ Commented Jun 15, 2023 at 6:47
  • $\begingroup$ @AloisChristen You can send shells sequentially $\endgroup$ Commented Jun 15, 2023 at 8:45
  • $\begingroup$ "You can't really tell how many times a shell hit someone. Due to this, you also cannot reuse shells". From the phrasing, it sounds like you cannot reuse shells only if they have already hit someone. Like they get forever marked by touching someone. Can you reuse a shell that returns to you without hitting someone? $\endgroup$ Commented Jun 15, 2023 at 18:38
  • $\begingroup$ @JasonGoemaat Yes $\endgroup$ Commented Jun 15, 2023 at 18:47
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    $\begingroup$ This puzzles starts out very interesting, but the solution is a bit disappointing :( was expecting some more problem solving, probably make a sequel? :D like how to give instructions to them so that wherever they are, they can meet/exit, etc. $\endgroup$
    – justhalf
    Commented Jun 16, 2023 at 2:34

1 Answer 1


Even with an unlimited number of shells, it is impossible to guarantee locating both individuals.

If one of them is at A, and the other is nowhere in the maze that can be reached before hitting A, then you have no way to distinguish between all the B locations, as any shell passing through them has already hit A.
enter image description here

  • $\begingroup$ What if you can discount where A and B are in the same corridor because they could see each other and don't mention that? $\endgroup$ Commented Jun 15, 2023 at 18:41
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    $\begingroup$ @JasonGoemaat that would only remove one of the B possibilities. You still have no way to check the remaining four. $\endgroup$
    – fljx
    Commented Jun 15, 2023 at 19:01

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