Puzzle: Knights and Pages

[Update: Click here for the solution and analysis]

I am a regular reader of Richard Wiseman‘s blog, including the weekly Friday Puzzle (the answer to which is always given on the following Monday). The puzzles vary in quality, and often leave me unimpressed, but other times they are very interesting challenges.

About seven months ago, I sent Richard a puzzle that I thought would be well suited to the weekly challenge. At the time he told me he would definitely use it, so I mentioned it to the community of Friday Puzzle blog post commenters, saying that some day a puzzle I’d submitted would show up. However, one cannot wait forever — I’ve got a lengthy analysis for the maths geeks that’s been waiting in my drafts, and I can’t unveil that until I first unveil the puzzle.

So last month, as we passed the six-month anniversary of the day I submitted it, I realised it was time to make a decision. I’m revealing the puzzle on this blog, and I’ll discuss the solution in a seperate blog post next week (along with that analysis I mentioned).

The puzzle comes via the book The Chicken From Minsk And 99 Other Infuriating Brainteasers by Yuri B. Chernyak and Robert M. Rose (previously mentioned in my Bookmash post). It resembles the famous wolf/goat/cabbages puzzle, but is more interesting. Here it is:

  1. Many years ago, three knights waited to cross the river Neva. Each knight had his own page, so there were six people. The boat they had could only carry two. However, the knights were ferocious killers and the pages were terrified. In fact, it was certain that any one of the pages would die of heart failure if he were not protected at every instant from the other knights by the presence of his own master. Was there any way to cross everyone over the river without losing a page?
  2. Suppose the previous problem involved four pairs of knights and pages. Is there a solution?
  3. Reconsider the previous problem with four pairs of knights and pages, but with an island in the middle of the river. With the island, is there a solution?

When commenting below, please do not give away any information about the answers. Not even hints. But you can talk about how hard you found it, the strategy you used, and things like that. I love puzzles where there are many different ways to solve it but they all lead to the same answer. For example, some people might solve it algebraically, using symbols to represent the characters, while others might prefer to draw a diagram of the situation and shuffle coins around. And within these methods there are many variations. Also, if you tried more than one strategy, it might be interesting to talk about the ones that didn’t work.

Obviously the answer to Part Two is “no”, otherwise there wouldn’t be any point in asking Part Three. But the interesting thing is how you go about proving it. You could simply write down all possible moves until every branch leads to a dead end, but I will give bonus points if you can prove it in a more interesting way. (Don’t post it here, though. Wait for my follow-up blog post next week.)

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3 Responses to “Puzzle: Knights and Pages”

  1. ElshaHawk Says:

    Those are the puzzle on Professor Layton that I do and breathe a sigh of relief that it is over! I can’t remember my moves! It always tells me it can be solved in as few as 11 moves or some such tiny number that I triple or quadruple before the puzzle clears…
    Yeah I’m no good at rubiks cubes either..
    The riddles I chose for my children’s novel are much simpler. :)

    Oh and, being American, moot is always ‘of no practical consequence’ or already disproven. There is no debate. It’s moot. Done. Finito.

  2. rhiggs Says:

    There are a number of details missing before one can attempt the puzzle…

    – Is the only stipulation that a paige cannot be in the boat with a knight that is not his master? That is, are all other pairings – knight/knight and paige/paige – OK to proceed without conflict or heart failures?

    – In the wolf/goat/cabbage puzzle, neither of the 3 are needed to row the boat. I assume in this puzzle one of the party always needs to be in the boat to row it (otherwise it would be ridiculously easy)?

    – Assuming the above, can both the knights and the paiges row the boat?

    – Can a knight and an unassociated paige be swapped with each other if one is in the boat and one is on land so that this doesn’t result in heart failure? I ask because technically they would be passing each other without the protection of the paige’s master.

    Thanks

  3. Flesh-eating Dragon Says:

    Elsha – practically no-one can do rubik’s cubes. :-)

    Rhiggs – Knights are never in danger from other knights (unless they threaten the wrong page, of course), and pages are never in danger from other pages. The boat can’t cross the river without at least one character in it, and all characters are capable of rowing the boat. As for the final question, I don’t see the problem. As long as the boat is on one side of the river and not in transit, characters in the boat are on the same side of the river as the boat. The boat itself is not a barrier that protects anyone or prevents anyone from being protected. Hope that helps.


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