Logicats Hints and Tips

Conventions

 * P and Q are used to refer to any (sub)statement of the form "statement X is true/false".
 * NOT(P) says to flip true for false and vice versa. So "statement X is true" -> "statement X is false" and "statement X is false" -> "statement X is true".

Rules

 * P and Q: true if both are true, false if either (or both) are false.
 * P or Q: this is true if either or both are true (i.e. this is an "inclusive or"). When false, this implies NOT(P) and NOT(Q)
 * "Exactly one of ... is true/false": true if both have different truth values, false if both are the same.

Statements that are automatically true/false

 * P or NOT(P): true. For example, "Statement X is true or statement X is false"
 * P and NOT(P): false. For example, "Statement X is true and statement X is false"
 * "There are less than one true statements": false

Statements that refer to themselves

 * "X: Statement X is false and Q": false. Additionally, it implies NOT(Q)
 * "X: Statement X is false or Q": true. Additionally it implies Q
 * "X: Exactly one of statement X or statement Y is true/false": Y is false (no conclusion on X yet)

Solving the puzzle

 * 1) Answer the questions that are automatically true/false.
 * 2) Answer the questions that you are now sure are true/false due to the answers in (1) (e.g. in (1) you answered X: false, and there's a statement that says "Statement X is true"). Repeat until you run out of sure answers.
 * 3) Now you've got a question and you're not sure of the answer. Guess. Prefer guesses that give you more moves to make (e.g. if it's a P or Q question I'll guess false, since this gives me two more answers that fall out from that one). Goto (2).
 * 4) You hit a contradiction. "X: Statement Y is true": true and "Y: whatever": false. Oops. One of your guesses was wrong. Undo your answers until you come to the last guess you made, then guess the other way. Or if you have terrible memory like yours truly, reset everything and start back from (1).
 * 5) You've answered all the questions. Great! Before submitting, go through the answers one more time and verify they're all consistent. If they are, submit and enjoy your bonus production. If you find an inconsistency, goto (4).

Advanced techniques
X must be false: if it were true, then Y is both true (from Y 's standpoint) and false (from X 's standpoint).
 * Sometimes pairs (or triples, or ...) of questions imply a certain answer, or at least certain restrictions. A set of statements that cannot all be true at the same time, plus a statement on the number of true/false statements.
 * An actual example:
 * X: Exactly one of statement X and statement Y is true/false
 * Y: Statement X is true