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Pastimes : Brain Teasers.
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To: Bob Bryenton who wrote (26)11/21/1996 10:54:00 AM
From: Dutch Red   of 136
 
Bob,

Doing this in just 3 weigh-ins includes 2 possible scenarios. You are
right in dividing the 12 balls in groups of 4 balls. For simplicity
I'll divide the 12 balls this way :

1 2 3 4 ... 5 6 7 8 ... 9 10 11 12

Now, let's say ball #11 is the odd ball and is 'heavy'.

---------------------------------------------------------------------
SCENARIO #1

step-a) weigh 1 2 3 4 vs. 5 6 7 8
result: 'equal' Now we know that the above 8 balls
are 'good' balls. Group 9 10 11 12 has the odd ball.

step-b) take any 3 good balls, weigh against any 3 of the last
4 balls.

i) 1 2 3 vs 9 10 11
result: 9 10 11 is heavier. we now know that odd ball
is in these 3 balls and that it is heavy ! Then
just weigh 9 vs 10 which results in 'equal'
leaving 11 as the odd heavy ball. Or, weigh
9 vs 11 or 10 vs 11 which points to 11 as
the heavy odd ball !

ii) 1 2 3 vs 9 10 12
result: 'equal'. you get lucky ! with just 2 weigh-ins
you find #11 as the odd heavy ball !

----------------------------------------------------------------------
SCENARIO #2 You're just unlucky and weighed...

step-a) 1 2 3 4 vs 9 10 11 12
result: 'unequal'. Either one of the balls in (1 2 3 4)
is lighter or one of ( 9 10 11 12 ) is heavier ! But you
do know that 5 6 7 8 are 'good' balls !

... I'll let you think about solving this scenario before giving the
answer. Hey, that's why we call it a BRAIN TEASER...

Dutchred
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