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Solution:
Number the pebbles 1 to 12
For the showtime weighing allow us set on the left pan pebbles
1,2,3,4 as well as on the correct pan pebbles 5,6,7,8
There are 2 possibilities. Either they balance, or they don't.
Case 1:
If they balance, as well as then the pebble to survive constitute is inwards the grouping 9,10,11,12.
In our moment weighing nosotros would set 1,2 inwards the left pan as well as 9,10 on the right. If these ease as well as then the pebble to survive constitute is either xi or 12.
Weigh pebble 1 against 11. If they balance, the required pebble is set out 12. If they produce non balance, as well as then xi is the required pebble.
If 1,2 vs 9,10 produce non balance, as well as then the required pebble is either ix or 10.
Again, weigh 1 against 9. If they balance, the required pebble is set out
10, otherwise it is set out 9.
Case 2:
if the showtime weighing 1,2,3,4 vs 5,6,7,8 does non balance?
Then whatever ane of these pebbles could survive the required pebble. Now, inwards fellowship to proceed, nosotros must maintain rails of which side is heavy for each of the
following weighings.
Suppose that 5,6,7,8 is the heavy side. We instantly weigh 1,5,6 against
2,7,8. If they balance, as well as then the required pebble is either three or 4.
Weigh four against 9, a known bad pebble. If they ease as well as then the required
pebble is 3, otherwise it is 4.
Now, if 1,5,6 vs 2,7,8 does non balance, as well as 2,7,8 is the heavy side,
then either seven or eight is a required, heavy pebble, or 1 is a required, lite pebble.
For the 3rd weighing, weigh seven against 8. Whichever side is heavy is
the required pebble. If they balance, as well as then 1 is the required pebble. Should the weighing of 1,5, half dozen vs 2,7,8 demo 1,5,6 to survive the heavy side, as well as then
either five or half dozen is a required heavy pebble or 2 is a lite required pebble. Weigh five against 6. The heavier ane is the required pebble. If they balance, as well as then 2 is a required lite pebble.
