Home > Logic > Liars and Knights
| Burger Buddies (Posted on 2003-11-27) |
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Three people decide to go out for burgers. They are either Knights, which always tell the truth, Knaves, which tell truths and lies in an alternating pattern, or Liars, which always tell lies.
They each want a burger, and want to get 4 toppings from the list of 7 (ketchup, mustard, onions, relish, tomato, cheese, lettuce) and give their order as follows:
A: I want ketchup, mustard, onions, lettuce, relish.
B: A wants tomato too, and he doesn't want mustard. I want ketchup, tomato, cheese, lettuce.
C: B doesn't want ketchup, and he doesn't want mustard. A doesn't want relish. I want mustard, tomato, cheese, lettuce.
After giving the orders to the burger cooker, he figures out what they want.(as anyone who can cook well must be really intelligent)
If all three people didn't all want a certain topping, what do the three people actually want as their four toppings on their burger?
(Note: I placed commas and periods to remind that each item/statement separated by commas is a separate statement.)
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Submitted by Gamer
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Rating: 4.2000 (10 votes)
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Solution:
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Because all three people are either Knights, Knaves, or Liars, every other statement has equal logical equivalence. In other words, every other statement is true or false. This means the statements can be broken up into two groups.
A: ketchup, onions, relish
A: mustard, lettuce
B: A-ketchup, ketchup, cheese
B: A-not-mustard, tomato, lettuce
C: B-not-ketchup, A-not-relish, tomato, lettuce
C: B-not-mustard, mustard, cheese
Assume A's second series is true. Then A's first series must be false (or he would have 5 toppings which isn't allowed), Then B's second series must be false because A wanted mustard, and B's first series must be false because A didn't want ketchup. This leaves B with less than 4 ingredients, and so A's second series must be false.
This means A's first series is true and his second series is false. This means both B's series are true, and C's first series is false and second series is true.
= k m o r t c l
A + - + + ? ? -
B + ? ? ? + + +
C ? + ? ? - + -
Because not all three wanted a certain topping, we can see C didn't want ketchup and A didn't want cheese. So:
A wants ketchup onion relish tomato
B wants ketchup tomato cheese lettuce
C wants mustard onion relish cheese
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