13 球称3次,有1/12的几率测不出坏球是轻还是重.12球的解如下,证明我还是没有患老年痴呆!
称蛋题正解
no drink today, here is the solution:
three groups: A 1234, B 1234, C 1234
first weighing: A vs B
1. if A = B
second weighing C1 + A1 vs C2+C3
1.1 if C1+A1=C2+C3
third weighing A1 vs C4
tells C4 under or over weight
1.2 if C1+A1 < C2+C3
the C1 under weight or C2/C3 over weight
third weighing C2 vs C3 will tell
2. if A1234 < B1234
second weighing A1+B1+C1 vs A2+A3+B2
2.1 if A1+B1+C1 = A2+A3+B2
then A4 under weight or B3/B4 over weight
third weight B3 vs B4 will tell
2.2 if A1+B1+C1 < A2+A3+B2
then A1 under weight or B2 over weight
third weighing A1 vs C1 will tell
2.3 if A1+B1+C1 > A2+A3+B2
then A2/A3 under weight or B1 over weight
third weighing A2 vs A3 will tell
