sharara
Age: 124
8202 days old here
Total Posts: 5253
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United Arab Emirates, United Arab Emirates
Hoor.. im here.. dekte hain KAUN rokta hai tumhe aane se... aao and be my guest.. waise to sparky ne nahi bulaya.. warna i wudve come with u to her shaadi tooo
sharara
Age: 124
8202 days old here
Total Posts: 5253
Points: 0
Location:
United Arab Emirates, United Arab Emirates
SOLUTION: ---------------------------------------------------------- Divide the 12 balls into 3 groups of 4. Name them group A, group B, and group C. Take group A and set it on the left of the scale, and set group B on the right of the scale:
A B
oooo oooo (1) \----/ \----/ | | \_____________/
Now if the weight is balanced, then set group A and B aside and take two balls from group C (which you know must contain the oddball) and set one on each side of the scale and take two balls from group B and set one on each side of the scale:
C B C B
o o o o (2) \----/ \----/ | | \_____________/
If the weight balances here, then take 'C' ball from the two that you left aside, place it on the right side of the scale, and take a ball from group B and place it on the left side of the scale:
B C
o o (3) \----/ \----/ | | \_____________/
If this balances, then the oddball is the last ball left in group C. If there is an imbalance, then the oddball is the group C billiard ball currently on the scale.
This is just one possible course of events, so backtrack to figure 2. If the weight does not balance there, then remove a 'C' ball from one side and a 'B' ball from the other side. If it balances now, then the C-ball that you just set aside is the odd one out, and if it does not balance, then the C-ball currently on the scale is the odd one out.
Now let's backtrack all the way to figure 1. The other possibility is that group A and group B will not balance. In that case, remove three A-balls from the left side, move 3 B-balls from the right side to the left side, and add 3 C-balls on the right side of the scale:
BBBA CCCB
oooo oooo (4) \----/ \----/ | | \_____________/
If the scale stays in the same tilt, then you know that the oddball is one of the two that did not change position from figure 1. The only two that did not change position are the A-ball on the left side and the B-ball on the right side, so it has to be one of those. Simply place that A-ball on the left side and put a C on the right, and if it balances, then the B-ball is the oddball, but if it does not balance, then the A-ball is obviously the odd one.
case 1)If the scale balances perfectly, then the oddball must be in the group of 3 A-balls that you removed from the left side in going from figure 1 to figure 4.
case 2)If the scale tilts in the opposite direction, then the oddball must be in the group of 3 B-balls that you moved from the right side to the left side.
For both cases, you can figure out whether the oddball is heavier or lighter than the normal weight, so place one of the three on the left side, the second of the three on the right side, and leave the last one aside for a moment. If the two balance, then the oddball is the one you set aside. If they don't balance, the oddball is the one that is on the appropriate side of the tilt.
