Paladins Puzzles No.3

Paladin

You have 9 snooker balls.
All appear identical.
One of them however is a slightly different weight to the others but feels the same to ure hand.
This ball is either lighter OR heavier. You dont know.
To determine the odd ball ( ) you have a balance scales.
You must find the ball in three weighings or less.
How can you do it?
Answers must explain FULLY how this is done.

Cloud

I think I have this one...

Okay let's say we have three groups of three balls, A, B and C...

There are a number of cases...

A and B same weight
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Weighing One

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First, take A and B and weigh them.

If A and B are the same, the odd ball is in C.

We call the C group C1, C2 and C3.

Weighing Two

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Then take two balls from C and weigh them (e.g. C1 and C2). If C1
is the same as C2, then C3 is the heavier or lighter ball. If they
are different, then take C2 and C3.

Weighing Three

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If C1 was heavier than C2, then if C2 is lighter than C3, C2 is the
lighter ball [C2=odd]. If C1 is lighter than C2, then if C2 is
heavier than C3, C2 is the heavier ball [C2=odd]. If C2 is the same
weight as C3, then C1 is the heavier or lighter ball [C1=odd].

.
.
.

A and B not the same weight
===========================
Weighing One

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Now if A and B were not the same weight, well then we know that the
odd ball is in either A or B.

Weighing Two

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So we take say group B, and weigh it against C. If it's the same
weight as C, the odd ball is in A. If not, the odd ball is in B
(since B cannot be different from both A and C and not have the odd
ball). Let's call the group that ball is in (be it A or X. You
should now know whether the odd ball is lighter or heavier:

If A > B and B < C, ball is lighter.
If A > B and B = C, ball is heavier.
If A < B and B > C, ball is heavier.
If A < B and B = C, ball is lighter.

Weighing Three

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Take two balls X1 and X2 from group X (X1, X2 and X3). Going on
the condition above, if X1 is not the same as X2 you should know
which ball is heavier or lighter (and therefore the odd ball).
Otherwise, if X1 is the same as X2, X3 is the odd ball.

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Where do you want to go inniu?

[This message has been edited by Cloud (edited 23-02-2000).]

WhiteWashMan

2 wieghs

3 sets of three. weigh 2 sets. if they are equal then the odd ball is in the 3 set
weigh to balls from the third set..if they are equal then its your last ball
hey presto

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One of Your Imps Does A Great Impression Of You
He Can Even Do The Ears....

Cloud

Well that's one case - it can't always be done in two, that's just your pure optimism!

Paladin

Pretty good C
How long did it take?
Enjoyed it I hope

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One ring to rule them all, One ring to to find them,
One ring to bring them all and in the darkness bind them

WhiteWashMan

actually its the same in all cases john...
no matter what whay you look at it it can be done in 2 weighs

Paladin

Im afraid ure wrong wwman
You need 3 weighings to cover all scenarios.
There are only one or two that cover 2 weighings

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One ring to rule them all, One ring to to find them,
One ring to bring them all and in the darkness bind them

Cloud

Well it took about 10 minutes or less to figure out, but more like 20 minutes to type up

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Where do you want to go inniu?