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classic weighing, comments on solution

(c) as we can see from our chart above, if the ABE/CDF weighing comes out with ABE low, then the situation is either: C is the light pill, D is the light pill, or E is heavy pill.

so in either situation (b) or (c), we have two possible light pills and one possible heavy pill. what we do in that case is we put one of the possible light pills and the possible heavy pill on one side of the scale, and two NORM pills on the other side of the scale. this is our third weighing. if it comes out even, then we know that the other possible light pill is the abnormal pill. if it comes out with the two NORM pills high, then we know that one of the pills on the other side is abnormally heavy, so we know that the possible heavy pill is the culprit. if it comes out with the two NORM pills low, then we know that one of the pills on the other side is abnormally light, so we know that the possible light pill on the scale is the culprit.

Comment 1: Just weigh C against D.
If the balance is even, then E is heavy pill;
If one pill is high, then it is light pill


that takes care of case (1), where the first weighing came out uneven.

what about case (2), where the first weighing comes out even?

then we know the abnormal pill is one of I J K or L, and we have two weighings to find the abnormal pill in.

for our second weighing, we put I and J on one side of the scale, and two NORM pills on the other.

(a) if this comes out uneven, we know the abnormal pill is I or J; we weigh I against one NORM pill to see if I is abnormal and if it isn’t, we can conclude that J is the abnormal pill.

(b) if the IJ versus 2 NORM weighing comes out even, we know the abnormal pill is K or L; we weight K against one NORM pill to see if K is abnormal and if it isn’t, we can conclude that L is the abnormal pill.

Comment 2: In case (b), we could not tell whether the abnormal pill is heavy or light.
My solution: For 2nd weighing, Weigh IJK against 3 NORM pills.
1>It comes out even, then L is the abnormal pill.
For 3rd weighing, weigh L versus a NORM pill to see if it's light or heavy;
2>It comes out uneven, say IJK side is light.
For 3rd weighing, weigh I versus K.
i>Even, then J is the light pill;
ii>Uneven, say I side is high, then I is the light pill.

Pan, Wenyu
Thursday, September 19, 2002

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