To help you solve the maze, you are given 3 bombs. A bomb can be used to destroy one wall in the maze.
Your goal is to get from the start to the finish, with the help of your bombs. There is only one correct solution, so good luck!
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16$\begingroup$ Nice idea for a maze-variant. $\endgroup$– BmyGuestCommented Jul 27, 2020 at 19:12
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2 Answers
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My path (red blotches are bombs)
Explanation:
Here I have highlighted important walls in purple, splitting the maze into sections. Anywhere within a section is reachable without a bomb. Going between sections is impossible without a bomb
NOTE: Everything below this has been edited. I'm combining some suggestions made in the comments to give a better explanation. If you want to see the original unwieldy graph explanation, look in the edit history.
I've colored all of the sections touching (i.e. reachable by 1 bomb) the starting section blue, and all the sections touching the ending section orange. One bomb must be used to enter a blue section, and one bomb must be used to go from an orange section to the exit. That leaves only one bomb. This leftover bomb must be used to go from a blue section to an orange section. Lo and behold, there is one area where blue and orange touch,
sections 3 (blue) and 11 (orange).
Therefore the only solution is to enter the correct blue section with one bomb, move to the correct orange section with another, and finally move to the end section with the last bomb.
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6$\begingroup$ Very detailed answer. +1. The graph part was maybe a bit of too much extra work. One can actually quite nicely see the same in your purple-wall section image already, but it certainly didn´t hurt neither. $\endgroup$– BmyGuestCommented Jul 27, 2020 at 19:11
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4$\begingroup$ I totally agree that the graph was overkill, but I wanted a better explanation than "Look, there's the answer" $\endgroup$– bobbleCommented Jul 27, 2020 at 19:24
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5$\begingroup$ If you use as a given that the solution is unique, you find that when you go from a region to the next, it can only be between regions that touch on a single wall length. If not, you could just as well break the neighoring wall. With the purple walls drawn you can see that you always have ony one region to go to. $\endgroup$ Commented Jul 27, 2020 at 23:04
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3$\begingroup$ Once you have your purple picture, you can use uniqueness (the question says "There is only one correct solution") to show that you must go from section 1 to section 3 with which it shares only one section of wall, and likewise from there to 11 and then to 14. $\endgroup$– msh210Commented Jul 28, 2020 at 11:23
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4$\begingroup$ Once you had the graph I might have been more inclined to work from both ends simultaneously. The 1st and fourth regions are known (1 and 14). You can then make a list of candidates for 2nd based on what can be reached from 1 and for 3rd based on what can reach 14. You can then just check which of the possible 2nd regions can reach which possible 3rd regions and find there is only one matching pair. It feels like it is less overall work this way but maybe its just how my brain works. Your method is good though and I personally like the graph. :) $\endgroup$– ChrisCommented Jul 28, 2020 at 15:21
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My solution is to do something like a depth-first search to create maps of isolated parts of the maze. Once we do that, it's easy to see how those isolated maps can be connected to use only 3 bombs.
You have to follow Red, jump to Orange, then to Cyan, then to Magenta. I wasted way too much time on Paint...
Here's the path more clearly:
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1$\begingroup$ Welcome to PSE! You clearly have the kernel of a solution here...nice work! May I encourage you to expand your answer to show the actual path, and a demonstration that there is no other such path? The excellent solution recently given in puzzling.stackexchange.com/a/100349/69217 is an example of a great answer for this forum, or indeed the other answer provided by the same user to this question. $\endgroup$ Commented Jul 29, 2020 at 18:39
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$\begingroup$ @JeremyDover Thank you for the suggestion. Is it part of the puzzle to prove that there is only a single solution? I thought that was a given. $\endgroup$ Commented Jul 29, 2020 at 18:41
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2$\begingroup$ You bet. The better received answers here are those that demonstrate the logic behind the solution, versus "I just saw it". While it is likely there will be only one correct answer, mistakes do happen: a logic-based step-by-step solution will reveal it. Please don't take this as being too critical...you obviously followed a logical process to achieve your solution. But try to think of it this way: if you're going to all of the trouble to paint the maze like that, you want people to look at your solution and think "nice work". Just trying to give some tips to help you get there :-) $\endgroup$ Commented Jul 29, 2020 at 18:51