Puzzles

SudokuI don’t much like puzzles. They irritate me. If ever I do tackle a puzzle, I feel guilty afterwards for wasting time that could have been spent more productively, for example reading. Also, paraphrasing Groucho Marks, any puzzle that I can solve, probably wasn’t worth the trouble, anyway. Despite this, I find myself doing sudoku puzzles quite often. This is because on the way home, Tigger grabs a couple of free newspapers, opens them at the sudoko page, and hands me mine. We then sit on the bus (and sometimes later in Starbuck’s) solving sudoku. We so involved the other day that we nearly missed our stop.

I had this brilliant idea the other day. I guessed that to solve any sudoku puzzle, all you had to do was to transfer it to a grid big enough to allow you to write into each vacant square all the possible numbers that could go into it. You would then find, I reasoned, that for at least one square there would be only one number or, at least, within a local group of 9 squares, there would be only one square offering a particular digit. By filling in these values, and eliminating them from the corresponding row and column, you would finally complete the whole thing.

The best way to prove or disprove such a theory is to try it out. If the method worked, then you would be able to solve any sudoku puzzle, including those set in competitions. You might even become a famous champion. Don’t bother trying it. It doesn’t work. You end up with symmetrically placed pairs of squares that can all hold the same two digits and you need to solve one of those in order to solve the others. Back to the drawing board.

Here is a puzzle I remember from my childhood. It takes longer to describe than to do it but as it is a “free form” puzzle (i.e. the answer cannot be derived by working it out, only by creative thinking, it might appeal to some puzzle fans.

Picture an intrepid Victorian explorer in the heart of some unmapped foreignland. He comes to where the road forks. He knows that one fork is safe to follow, the other mortally dangerous. But which is which? Loitering near by he spies two tribesmen. Having done his homework, he knows that two tribes live in that region, one called Truthtellers because they always tell the truth, the other called Liars because they always lie. He has no way of knowing to which tribe or tribes the two natives belong. In that part of the world, etiquette allows a traveller to ask exactly two questions which must be of a kind that can be answered with yes or no. Which two questions does out traveller ask in order to be put on the safe road?

One question will obviously be something along the lines of “Is the right fork the safe road?” but what is the other question, the one that allows him to know the truth value of the answer? I know one solution. Maybe there are others.

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About SilverTiger

I live in Islington with my partner, "Tigger". I blog about our life and our travels, using my own photos for illustration.
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5 Responses to Puzzles

  1. tomeemayeepa says:

    I hate puzzles and logic was never my forte but wouldn’t just one question do? Using the count-the-sheep’s-legs-and-divide-by-four-method I’d ask ‘What would the other fellow say was the right way?’ and then take the other road.

  2. SilverTiger says:

    One way to tackle this is to tabulate the possible pairings and to note the answers you would get to each question. If a pattern emerges, the solution is found.

    For example, assuming T = Truthteller, L = Liar and the question is put to the tribesman on the left, we might get something like this:

    Question: Does he tell the truth?

    T T Yes
    T L No
    L L Yes
    L T No

    These answers do not help. For example, we get the answer “yes” for both a pair of Truthtellers and a pair of Liars.

    Your solution (recast as a yes/no question) is as follows (we assume that the right-hand fork is the safe one:

    Question: Would he say the right hand-fork was safe?

    T T Yes (Correct)
    T L No (Wrong)
    L L Yes (Correct)
    L T No (Wrong)

    So we receive two “yes” answers and two “no” answers. If we knew whether the tribesmen were Truthtellers or Liars, this would provide the answer we need. Unfortunately, we do not know this. Therefore we do not know whether the “yes” is a truthful “yes” and the “no” and mendacious “no” (equivalent to a truthful “yes”) or the other way about.

    I think we first need to know the status of the respondent so we know whether to take his answer as it is or take its negative.

    I will propose a solution tomorrow.

  3. tomeemayeepa says:

    Sorry, I didn’t read the problem with enough care. I would have to fall back on eenie, meenie, minie, mo (politically corrected, of course) and pray hard.

  4. SilverTiger says:

    The solution I thought up for the Truthtellers v Liars puzzle is shown below with its “truth table” and explanation. I don’t claim it is the only solution. In fact, as it is a “free form” type of puzzle, there are likely to be other solutions.

    We again assume that the question is put to the tribesman on the left.

    Question: Do you both belong to the same tribe?

    T T Yes
    T L No
    L L No
    L T Yes

    Note that, irrespective of the truth of the answer (and the third and fourth answers are false), when the answer is Yes, the second tribesman is a Truthteller, and when the answer is No, the second tribesman is a Liar.

    Armed with this knowledge, we can ask the second tribesman “Is the right-hand fork the safe road?”

    If he is a Truthteller, we accept his answer at its face value and if he is a Liar we take the opposite of his answer as true.

  5. tomeemayeepa says:

    Blindingly obvious when it’s explained. If only solving Spam were that easy. Hope you come up with some more of these- I’ll sit quietly in the back row and applaud when the time comes.

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