[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:
- 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?
- Suppose the previous problem involved four pairs of knights and pages. Is there a solution?
- 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.)