The Logic of Labyrinth

By: Jamie Bish& Michael Humbert

SUNY FredoniaAMTNYS 2009

1. You have ridden at least one of these three rides : the Superman, the Viper, the Predator.

2. If you rode the Superman but not the Predator, then you have ridden the Viper.

3. You rode both the Predator and the Viper, or rode neither.

4. If you rode the Predator, then you rode the Superman. 

S V P PVS )( VPS SP

)V P(

V)(P

F F F F T T T

T F F T F T T

F T F T T T F

F F T T T F F

T T F T T T F

F T T T T F T

T F T T T T F

T T T T T T T

• Application of Logic!

One guard always liesone always tells the truth.

One door leads to the castleone leads to certain death.

• The Key is Negation!

By asking what the other guard would say, we will always end up with a negation!

Who lies & who tells the truth?

It doesn’t matter!

Let L(X)= the negation function◦ (What the liar tells us)◦ L(X)=X

T(L(A)) L(A) A

T T F

F F T

L(T(A)) T(A) A

T F F

F T T

Let T(X)= the identity function(What the truth-teller tells us)T(X)=X

Let A = “Door ‘A’ leads to the castle”

Truth Table

• Nothing mystical about Mathematics

• Develop analytical reasoning skills

• Can be incorporated into manylessons throughout the year

• Use of visual aids to reinforcethinking abilities