Do you see the symmetry in the solution to this problem?
The cannibals and missionaries river crossing problem is a well known recreational math problem dating to the 19th century (before political correctness). Link
Spoiler Alert!
The solution has a nice symmetry that nobody ever seems to mention. The middle move has a missionary and cannibal crossing the river to go from position MMCC/MC to position MC/MMCC. Do your see anything interesting about this? If you had written down the previous moves, do you see how this would enable you to immediately solve the problem?
Keep in mind that at any point in the problem, if you do the previous moves in reverse order and in the reverse direction, you would end up back at the starting point.
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I am disappointed that I had no takers for this question. Let me explain what I found. I am hoping that anyone who had not seen this problem before could figure out what it was from the link.
The move I described moves from a position to another position such that the people on the near shore of the second position is the same as the people on the ffar shore of the first position, which means that people on the far shore pf the second position are the same as those on tne near shore of the first position. Additionally the position of the boat will be on the opposite side, meaning that it will be with the same group of people.
Let us use the word reflection to describe the relationship between the two posiitons. If P1 is the first position and P2 is the second position, we can say that P2=R(P1). Furthermore, for any position Q that can be reached from position P, R(Q) can be reached from R(P).
By doing moves in the reverse direction, we can get from P1 to the starting poition S. That means that we can go from P2=R(P1) to R(S). But R(S) is the end position of the puzzle and so we have found a way of solviing the problem.
Great classic puzzle. Have you done the Jealous husbands problem as well? very similar.
I have not done that one. Here is one you may find of interest. It has another symmetry. From any solution you can get another one by swapping father and mother, and son and daughter.
You can work on it interactively here
For this kind of questions, you’re better off answering it on StackExchange. Keep in mind that you must not know the answer and that you must list the steps you took to try to solve it.
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