Fair's Fair
Bill Fair's gaming booth at the state fair had an interesting game. On the counter in front of him were four overturned cups. Each concealed the same number of balls. On each cup was a statement about the number of balls underneath. From left to right the statements were:
one or four
two or four
two or three
one or two
Only one of the statements was correct.
Could you win a prize at Bill Fair's booth? How many balls were under each cup, and which statement was true?
one or four
two or four
two or three
one or two
Only one of the statements was correct.
Could you win a prize at Bill Fair's booth? How many balls were under each cup, and which statement was true?
Labels: logic
posted by Zaux at
10:24 AM
6 Comments:
This post has been removed by the author.
No more calls please ... we have a winner! ... heh heh.
Ooops, repost as had some typos in the explanation:
Call the cups A, B, C and D (in the same order that they were defined above).
Zero balls => no statement is true.
One ball => A and D would be true.
Two balls => B and C would be true.
Three balls => only C would be true.
Four balls => A and B would be true.
More than 4 balls => no statement is true.
So the only way that only one statement is true is if there were three balls under the cups.
Fair's Fair
Given:
-4 statements, only 1 true
-all cups have = number of balls
*1)=1 or 4
*2)=2 or 4
*3)=2 or 3
*4)=1 or 2
Call number of balls N
N=0,
*1 false, *2 false, *3 false, *4 false
invalid solution
N=1,
*1 true,*2, false, *3 false, *4 true.
2 trues, invalid
N=2
*1 false,*2 true, *3 true, *4 false
2 trues, invalid
N=3
*1 false, *2 false, *3 true, *4 false
valid solution
N=4
*1 true, *2 true, *3 false, *4 false
invalid solution
N>4,
*1 false, *2 false, *3 false, *4 false
invalid solution
Answer:
-Only valid solution is when N=3
-only true statement is " 2 or 3"
As far as winning a prize goes, the conditions for winning a prize were never stated in the question, thus the answer is indeterminate.
Cam
three...DUH
DUH?
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