Watch the video to see the puzzle
Scroll down to see the solution!
The solution (as written by Kestral thanks Kestral!)
Weigh 1 pair against 1 pair, and set the third pair aside.
There are 2 possible results: The scales are In or Out of balance.
IN BALANCE
You got lucky... the odd ball is one of the two you set aside.
Replace a pair on one side of the scale with the pair you set aside.
Note whether the new pair are lighter or heavier than the "normal" pair.
Weigh the 2 new balls against each other.
If the pair was lighter than the "normal" pair, the light ball is the odd one out.
If the pair was heavier than the "normal" pair, the heavier ball is the odd one out.
OUT OF BALANCE
This is the tougher option.
Note which side is heavier.
Swap 1 of the balls from the heavier side for 1 of the 2 "normal" balls you set aside.
There are two possible options: Change or No Change
CHANGE
Lucky! the removed ball is the odd ball and is heavy.
NO CHANGE
We know the ball you just swapped in is "normal" so the odd ball is one of the remaining original 3 still on the scales.
Weigh the 2 balls from the lighter side against each other.
Again, there are 2 possible results: The scales are In or Out of balance.
IN BALANCE
The removed ball is the odd ball and is heavy.
OUT OF BALANCE
The lighter of the two is the odd ball.
The key is the ball swap to determine whether the odd ball is light or heavy. It didn't take me very long... the majority of my time was spent in working out the wording and actually typing it in.
JV
12 Comments
Weigh 1st/2nd ball
IN BALANCE
Weigh the 3rd/4th ball
-----IN BALANCE
-----Weigh 1st/5th ball
----------IN BALANCE
----------6th ball is the odd ball
----------OUT OF BALANCE
----------5th ball is the odd ball
-----OUT OF BALANCE
-----Weigh 1st/3rd ball
----------IN BALANCE
----------4th ball is the odd ball
----------OUT OF BALANCE
----------3rd ball is the odd ball
OUT OF BALANCE
Weigh the 1st/3rd ball
-----IN BALANCE
-----2nd ball is the odd ball
-----OUT OF BALANCE
-----1st ball is the odd ball
Split the balls into three sets of two, lets call them A, B and C
Weigh A v B - (1)
~If they are even then you know that C has the irregular ball
~If they are uneven
Switch B for the C and weigh (2)
~ If the balance is now even, one of B is different
~ If they are still uneven, you know one of A is different
+ HERE IS WHERE YOU DETERMINE HEAVIER AND LIGHTER
One of the two sets was of regular balls. Whichever set tipped the scales, you can see if the irregular ball is heavier or lighter. Once you know what the regular weight is, it is easy to determine if the irregular one's weight.
Now knowing which set balls is irregular, take one of those balls and compare it to a known regular. (3)
~If the scales tip, then the ball from the irregular set is the one
~If the two are the same, then the untested ball is irregular
~Either way you already know if it is lighter or heavier
I think this is close to Kestral's way, just some slight changes!
You have 11 balls, one is lighter or heavier, which one is it?
Use scales three times.
Gl to all, take your time, you will need it! :P
Solution will be posted soon.
(Not that it matters.)
First, separate the balls into groups of three and compare them.
Take the three from the heavier side and add to them one from the lighter side.
Second, separate the balls into groups of two and compare them.
Take the heavier side and compare those two.
And, voila. The heavier side is...well, the heavier ball.
Weigh 2 pairs of 2 balls.
If balance: the pairs are normal; weigh 1 ball from 3d pair with a normal ball. If they are equal the last ball is imbalanced, if not then this ball is. Make a third weigh with a normal ball to find out in which way is the imbalance.
If imbalance: third pair is normal. Weigh third pair with lighter pair. If equal, then imbalanced ball is heavyer; Weigh one ball from the imbalanced pair with one normal ball and you get the imbalanced ball. If lighter (it can only be equal or lighter) then the imbalenced ball is lighter. Weigh one ball from the imbalanced pair with a normal ball and you get the imbalanced ball.
Hey you know AdGuy always gets the last word! ;)