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Explain this riddle. You have twelve balls, one weighs either more or less then the other 11. You have a scale but are only allowed to use it 3 times...Can you tell me which ball it is AND if it weighs more or less (Note: explain the logic you used to find the ball, explain all possible outcomes)?
Question
#23938. Asked by Hawk. (Nov 05 02 12:24 AM)
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SOTHC
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I will have to do this in bits as it will not send in one go.
Sorry Hawk but the replies seem to be bouncing around without getting anywhere near the answer you require. It is a bit long winded but here goes: -
Divide the balls into three groups of four each, AAAA, BBBB and CCCC.
Weigh AAAA-BBBB.
Possible results are: -
They balance: Means one of the C's is heavy or light.
Therefore, weigh CCC-AAA (all A's are now known to be standard):
They balance: Means the 4th C is the oddball.
Therefore, weigh the 4th C against any other ball.
4th C falls: Means The 4th is heavy.
4th C rises: Means The 4th is light.
CCC side falls: Means one of the C's is heavy.
Therefore, weigh C-C:
They balance: Means The other C is heavy.
One side falls: Means That C is heavy.
CCC side rises: Means one of the C's is light.
Therefore, weigh C-C.
They balance: Means the other C is light.
One side rises: Means that C is light.
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SOTHC
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The AAAA side falls: Means the oddball is either a heavy A or a light B and the C's are all standard.
Therefore, arrange the balls into three new groups like so: AAAC BBBA CCCB. Weigh BBBA-CCCB:
They balance: Means Oddball in AAAC.
Therefore, weigh A-A.
They balance: Means the other A in AAAC is heavy.
One side falls: Means that side is the heavy A.
Left side (BBBA) falls: Means the A in BBBA is heavy or the B in CCCB is light.
Therefore, weigh A-C (C is known to be standard).
They balance: Means The B in CCCB is light.
A side falls: Means A is heavy.
C falls: Not possible.
Right side (CCCB) falls: Means a B in BBBA is light.
Therefore, from BBBA weigh B-B.
They balance: Means the other B in BBBA is light.
Left side falls: Means the B on the right is light.
Right side falls: Means the B on the left is light.
The BBBB side falls: the oddball is either a heavy B or a light A and the C's are all standard.
Therefore, arrange the balls into three new groups like so: AAAB BBBC CCCA. Weigh AAAB-CCCA:
They balance: Means the oddball is in BBBC.
Therefore, weigh B-B.
They balance: Means the other B in BBBC is heavy.
One side falls: Means that side is the heavy B.
Left side (AAAB) falls: The B in AAAB is heavy or the A in CCCA is light.
Therefore, weigh B-C (C is known to be standard).
They balance: Means the A in CCCA is light.
B side falls: Means B is heavy.
C side falls: Not possible.
Right side (CCCA) falls: Means an A in AAAB is light.
Therefore, from AAAB weigh A-A.
They balance: Means the other A in AAAB is light.
Left side falls: Means the A on the right is light.
Right side falls: Means the A on the left is light.
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HAWK
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SOTHIC very very nice...I am impressed, this riddle can be tough as you get lost quickly in the logic necessary...
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thickheed
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Forgive me if I appear thick, but I've another {question;--} How many times did SOTHC use the scale?
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Son of The Household Cavalry
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Only three times but each time you use the scales there could be more than one outcome so I hope I gave all the possibilities as Hawk requested in the question. It just looks as if the scales were used more than they should be.
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