This my adaptation of a logic puzzle from Raymond Smullyan’s great book, What is the name of this book? It is not the hardest puzzle in the book, but it is the one that most successfully caught me out. I will give some more details on the background when I post the solution.
Maths knowledge required: None.
Puzzle: Evening is drawing in and you are lost in a dark forest. This is not an ideal situation, particularly given the frequent bloodcurdling howls that echo through the trees. Unless you can find your way out quickly, you will surely be devoured by the forest’s terrifying inhabitants.
Just when all hope seems lost, you spot a little cottage, almost hidden between the trunks. You hurry over and knock at the door, which opens to reveal a wizened little old lady, wearing a black pointy hat and carrying a broomstick.
Now, while you realise that dealing with pointy-hatted, broomstick-carrying old crones in the middle of dark forests is probably something to be avoided (particularly when you are a character in a fairy-tale-inspired narrative puzzle), you are also aware that beggars can’t be choosers, so you go ahead and ask the woman whether she can lead you out of the forest.
“I am too old to leave my cottage,” she replies, with a mischievous glint in her eye, “but I will happily send one of my grandchildren to guide you.” With this, she clicks her fingers and three gaunt figures shuffle out to stand beside her: a brother and two sisters, each about fourteen years old.
The children are in a pretty sorry state. One of the girls in particular is very pale, barely holding herself upright, with a terrible hacking cough. In all honesty, you are not certain that she could make it out of the forest at all, so how much use she would be as a guide is not certain. Her brother looks a little stronger and her sister stronger still, but you make a mental note to report the household to social services as soon as you get back to civilisation.
“All three know the way out of the forest,” the woman hisses, “but you must choose which of them to take as your guide. To make your choice, you may ask one question to one child, and your question must have a “Yes” or “No” answer. However, one child always tells the truth and one always lies. The third sometimes tells the truth and sometimes lies… and is a werewolf.”
This last piece of information naturally comes as a bit of a shock. With a full moon due, choosing a werewolf as your guide would be distressingly fatal. Set against the prospect of being torn limb from limb, whether you end up with a liar or a truth-teller seems pretty irrelevant.*
Your dilemma then is this: What question should you ask, which child should you ask it to and how should you act based on the answer you receive?
Follow-up question: If, instead, the woman had told you that the truthful child was the werewolf, how would this affect your strategy?
Please post comments/questions/solutions below. All comments are moderated, so no need to worry about giving away the solution.
* You can assume that any of the children would lead you honestly. It is only when answering questions that they respond in the ways that the woman has explained.
NOTE: Regarding the child who sometimes tells the truth and sometimes lies, you may assume that, whatever question is asked, there is always some chance that they will tell the truth and some chance that they will lie.
* – Not too taxing
** – Requires significant thought
*** – Extremely difficult
!!!! – Requires high level mathematics / Unsolved / Insoluble
Thomas Oléron Evans, 2015