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Sunday Puzzle-50

User Rating: / 8
Written by Administrator   
Sunday, 25 August 2013
Puzzle courtesy of Barry R. Clarke, columnist for The Daily Telegraph and international puzzle expert
Check out his new book "Mathematical Puzzles and Curiosities" on Amazon

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Fantasy Fortune
"What brings you here?" said a voice as Toddler Toby approached the red cave. There, high in a tree, sat the Wizard of the Wood. "I've come to seek my fortune," said Toby. Suddenly, a pixie, an elf, a goblin and a dwarf appeared in the cave entrance, each holding a black bag. "Then now is your chance," said the Wizard. "One of those bags holds 5000 gold coins, one has 3000, another 2000, and the fourth has none."

   "My bag and the goblin's have the highest and lowest amounts," said the pixie.

   "This bag and the pixie's have a total of 5000 coins," said the elf.

   "The dwarf's amount taken from my amount leaves 3000 coins," said the goblin.

   "Neither I nor the pixie have the highest or lowest amounts," said the dwarf.

   "And exactly two of them are lying," said the Wizard. "Choose a bag, but be careful, the bearer must be a truth teller or you cannot leave the wood."

   What is the highest amount Toddler Toby can take with him and from whom?

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Comments (1)
1. Written by O_x on 13:34 26 2013 .
The 4 given Statements can be written as: 
(1) (P=5000&G=0) OR (P=0&G=5000) 
(2) (E=2000&P=3000) OR (E=3000&P=2000) 
(E=5000&P=0) OR (E=0&P=5000) 
(3) (G=5000&D=2000) OR (D=0&G=3000) 
(4) (D!=0&P!=5000) OR (D!=5000&P!=0) 
& denotes the logical 'AND'  
OR simply means 'OR' :p 
Assume, (1) => TRUE: 
(P=5000&G=0) = TRUE, 
The other statements are FALSE. 
(P=0&G=5000) cannot be TRUE. 
So, statement (1) is FALSE. 
Which means. . . 
Pixie is the 1st Liar. 
I can do the same with (2) 
and conclude that: 
(E=2000&P=3000) and (E=3000&P=2000) can be TRUE when Goblin is the 2nd liar. 
The highest amount = 3000 
He has to take it from the Elf,(not Pixie) because Pixie is the liar.  
Tadaaaaa! :p 

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Last Updated ( Sunday, 25 August 2013 )
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