Monday, 13 January 2014

Sandcastle Builder - New Logicat Tricks

The logicat revamp came out and essentially invalidated my old posts about logicats.  Now you can just solve the puzzles!

But solving the puzzles is one thing, solving them fast is another.  Despite the fact that you can now get one correct answer per statement in the puzzle, and even despite the fact that you can "wager" more than one puzzle at once, you are still going to be solving a lot of puzzles.

So here are my logicat tips:

1. No Contradiction Means You Are Right
The algorithm generates puzzles with a single correct solution.  That means if there is no contradiction in the answers you have given then that is the one and only correct soluation.

2. Just Start Filling Things In
This is probably the most important tip.  Don't think things out a lot, just take a statement, mark it true or false and start going with what that implies.  Each time you assign a truth value to a statement verify that you haven't hit a contradiction.  If you have, you know the first statement you marked is the opposite of how you marked it.

3. Self-Referential Statements
X: ~X or Y means that X is true and so is Y.
X: ~X and Y means that X is false and so is Y.
These are either great starting points to the whole puzzle or the solution to sub-puzzles.

But what about X: X or Y and X: X and Y?  A not-uncommon puzzle you will receive is one where there is only one statement of one of those forms and all the other statements make only a single claim.  When you see a puzzle like this, you know immediately that if X is an "or" statement then Y false and if it is an "and" statement then Y is true.  How do you know that?

Suppose I have a puzzle that says:
X: X or x(Y)
Y: y(Z)
Z: z(W)
W: w(X)

Suppose X was true.  That would mean that either W is true and w(X) = X or W is false and w(X) = ~X.  At any rate, w() will determine what the truth value of W is.  We can similarly go back through Z and Y and get a truth value for Y and hence x(Y).

If x(Y) is true, then we have a problem.  You see, you could change x(Y) to be false which would reverse the truth value of Y and that would reverse Z and W as well.  So it would finally reverse X.  But the problem is that set of statements would contain no contradiction.  If X is false then x(Y) is false and all the other statements line up correctly.  Thus, the puzzle would have two solutions, which is not allowed.  It's pretty easy to reverse this argument for and-statements.

So, if you see a puzzle like the one above, mark Y false and follow the conclusions through to determine if X is true or false.

4. If You Get Something Wrong, Give Up
This is not necessarily good advice.  But when your Automata Control is high enough and you have Zookeeper, by the time you've failed to solve a puzzle and been given a second chance, you can just hit clear answers and then submit and move on to the next one.  If puzzles are at a premium then obviously this isn't a good idea.  Also, clearly, if you got everything wrong it is pretty easy to solve.  But if I got two of seven statements wrong why would I read the same puzzle over again looking for a mistake I made when my mind is already clouded by a proposed solution.  I find it much better to start fresh.

5. If You are Getting Things Wrong, Go to Bed
The best of us are not above a misclick, but if at some point it's not just a misclick.  Go to bed already.

3 comments:

  1. #5 is my solution to everything and has singlehandedly gotten me where I am today.

    ReplyDelete
    Replies
    1. You are a wise one, Master Bennett.

      Delete
  2. I struggle with logic; this post was extremely helpful for me. =)

    ReplyDelete