Brain Teasers
Is it Fair
At the fairground, Ben was watching a cup and balls trick. The stall owner had labeled the cups A-D. There was a total of four balls under the cups. The owner made the following claims:
"There is 1 ball under cup A, zero or 1 ball under B, 2 balls under C, and zero or 2 balls under D."
In reality, no cup had more than 2 balls underneath and exactly three of his four claims were lies. If we know that cup A had no balls underneath, how many balls did each cup have?
"There is 1 ball under cup A, zero or 1 ball under B, 2 balls under C, and zero or 2 balls under D."
In reality, no cup had more than 2 balls underneath and exactly three of his four claims were lies. If we know that cup A had no balls underneath, how many balls did each cup have?
Answer
A=0B=2
C=0
D=2
We know that claim 1 is a lie because A has no balls under it.
If claim 3 is true, then C has 2 balls under it, which would mean that either B or D would have to have 2 balls under them, or they would each have 1 ball. This means that if claim 3 is true, then either claim 2 or claim 4 would also be true. Also, if C had 1 ball, then B has 1 and D has 2 which makes claims 1 and 4 true, or B has 2 and D has 1 which makes all claims lies. As only one claim is true, then this means that claim 3 must be false and C must have 0 balls.
This means that both B and D must have 2 balls, which means that claim 2 is a lie and claim 4 is true.
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Comments
1 ball under c and 3 under D also seems to be a solution .. am I right? .. liked the mental exercise .. thanks for thinking it up and sharing .. now I need a brain break .. where's the coffee!
Oww.. my brain hurts. Too many letters and numbers in the same teaser.
D can't have 3 balls; one of the puzzle axioms is that no cup has more than two balls under it. However, 2-0-1-1 is also a solution -- there's a hole in the logic where the author explains that C can't have exactly one ball; he hasn't covered all the possible cases.
Yep .. I read right past that no greater than 2 balls axiom (I like that word!) .. however, we also somehow know (per the problem set-up) that cup A has no balls (is this another axiom?.. I'll have to axiom...) so 2011 violates the problem definition too..and if we know the owner lied three times, we're clairvoyant! We can just know the solution! .. so, I still think it is a good logic problem and rated it so. Darned axioms!
Thanks for posting everyone!
May 11, 2005
it is not hard, just read carefully
It is hard, but must be read carefully. Forget the axioms! Enjoyed this one! Thanks!
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