There are 9 coins. Out of which one is odd one i.e weight is
less or more. How many iterations of weighing are required
to find odd coin?
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Answer / vivek rai
Only 2 iterations required.
1- Take 6 coins and weigh 3 against 3
2- if it is equal then havier coin will in rest of 3 coin.
then we take 2 coins in rest of 3 coin and weight.
3- if it is eqal then rest 1 coin is havier.
| Is This Answer Correct ? | 31 Yes | 11 No |
Answer / devendra singh
there are maximum two iterations in which the odd coin can
be found out
firstly weigh 3-3 coins and then there are two possibilities:
if they turn out two be equal that means the odd coin is in
the remaining 3 coins and then we can weigh any two coins
from the remaining 3 coins and if they are equal the left
one is odd and if they are not equal the one which is less
heavy or more heavier according to the problem will be the
odd one..
in the second condition if the 3-3 coins weighed earlier are
not equal then then the side of 3 coins which is heavier or
lighter as described in the problem will be taken and and
two coins from that will be weighed and as said earlier the
odd one can b spotted ...so just two weighings required.
| Is This Answer Correct ? | 3 Yes | 1 No |
Answer / guest
It is always possible to find odd coin in 3 weighings and to
tell whether the odd coin is heavier or lighter.
1. Take 8 coins and weigh 4 against 4.
o If both are not equal, goto step 2
o If both are equal, goto step 3
2. One of these 8 coins is the odd one. Name the coins on
heavier side of the scale as H1, H2, H3 and H4. Similarly,
name the coins on the lighter side of the scale as L1, L2,
L3 and L4. Either one of H's is heavier or one of L's is
lighter. Weigh (H1, H2, L1) against (H3, H4, X) where X is
one coin remaining in intial weighing.
o If both are equal, one of L2, L3, L4 is lighter. Weigh L2
against L3.
? If both are equal, L4 is the odd coin and is lighter.
? If L2 is light, L2 is the odd coin and is lighter.
? If L3 is light, L3 is the odd coin and is lighter.
o If (H1, H2, L1) is heavier side on the scale, either H1 or
H2 is heavier. Weight H1 against H2
? If both are equal, there is some error.
? If H1 is heavy, H1 is the odd coin and is heavier.
? If H2 is heavy, H2 is the odd coin and is heavier.
o If (H3, H4, X) is heavier side on the scale, either H3 or
H4 is heavier or L1 is lighter. Weight H3 against H4
? If both are equal, L1 is the odd coin and is lighter.
? If H3 is heavy, H3 is the odd coin and is heavier.
? If H4 is heavy, H4 is the odd coin and is heavier.
3. The remaining coin X is the odd one. Weigh X against the
anyone coin used in initial weighing.
o If both are equal, there is some error.
o If X is heavy, X is the odd coin and is heavier.
o If X is light, X is the odd coin and is lighter.
| Is This Answer Correct ? | 7 Yes | 7 No |
Answer / saint
3 Iterations are required if you do not know if the odd
coin is lighter or heavier when you start. This is a nice
simple to follow process;
Divide coins into three piles of three, A, B & C
Weighing 1
-----------
Weigh piles A and B, and note which is the heaviest, or if
equal weight
Weighing 2
-----------
Weigh piles A and C, and note which is the heaviest or if
equal weight
If A does not equal both B and C, then A contains the odd
coin.
If A = C but does not equal B then B contains the odd
coin.
If A = B but does not equal C then C contains the odd
coin.
Having established which pile contains the odd coin, then
determine if it the odd pile is lighter or heavier by
looking at the results of the first two weighings
A = Odd pile
--------------
If A is the odd pile, then if it weighed less than B and C
in the first two weighings, then the odd coin is lighter,
else it is heavier
B = Odd Pile
------------------
Use the results of Weighing 1 and compare B with A. If A
was the lighter pile, then the odd coin is Heavier than the
rest, if A was heavier then the odd coin is Lighter
C = Odd Pile
------------------
Use the results of Weighing 2 and compare C with A. If A
was the lighter pile, then the odd coin is Heavier than the
rest, if A was heavier then the odd coin is Lighter
Weighing 3
-----------
Now take the pile that contains the odd coin, take two
coins out and weight them against one another
If the coins match, then the remaining coin is the odd coin
Else if the coins do not match, then if we are looking for
a lighter coin, then the lighter coin is odd, and if we are
looking for a heavier coin, then the heavier coin is odd!
-------------------------------------
| Is This Answer Correct ? | 5 Yes | 5 No |
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