From: PL436000@BROWNVM.BITNET (Jamie)
Newsgroups: bit.listserv.politics
Subject: Stalinist Purge of the Bad Apple: the solution revealed
Date: 13 Nov 92 16:00:47 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU

>From:         KIS100F@SMSVMA.BITNET

>There are 12 identical looking apples.
>
>11 of them weigh exactly the same.
>The 12-th of them is defective (such as: liberal or conservative) in the
>sense that it is heavier or lighter than the rest of the apples.
>The apples are shuffled and get randomly arranged.
>
>An ordinary 2-pan balance is provided.
>Exactly 3 weighing chances are given.
>Determine the defective apple AND also tell whether the defective apple
>is heavier or lighter (ie liberal or conservative).
>(over)

Your Logic Czar feels that it is incumbent upon him to show how simple
the problem really is. Can't have all of our other Czars and elected
officials worrying their pretty heads about it.

Choose 8 apples. Weigh four of them against the other four.

    Case 1: They balance against each other. Then the defective
            one is among the other four.

         Then take three of those four, and balance them against
         three of the apples that you know are good ones.

              Case 1.1 They balance. Then the defective one is
                        remaining. Check it against a good one
                        to see whether it is heavy or light.

              Case 1.2 The good three are heavier. Then we know
                       the defective apple is light and is one of
                       three. Balance one of those three against
                       another.

                 Case 1.2.1 They balance. Then the defective one
                            is the third, and is light.

                 Case 1.2.2 They don't balance. Then the lighter
                            of the two is defective.

              Case 1.3  The good three are lighter. Then proceed
                        as in case 1.2, but the bad apple is heavier.

       Case 2: They don't balance. Call the heavier four apples
               "Batch A," the lighter four "Batch B," and the
               remaining four "Batch C." Label the Batch A apples
               "A1" "A2" A3" and "A4," and likewise for the B Batch.
               (Don't bother labeling the C apples. We know they
                are good apples.)

         Now put A1, A2, B1, and B2 in one pan, and A3, B3, and two
         of the C apples in the other.

         Case 2.1 The side with the C apples is light. Then, either
           A1 or A2 is a defective heavy apple, or B3 is a defective
           light apple. So weigh A1 against A2.

           Case 2.1.1 They balance. Then B3 is defective and light.

           Case 2.1.2 A1 is heavier. Then it is defective and heavy.

           Case 2.1.3 A2 is heavier. Then it is defective and heavy.

        Case 2.2  The side with the C apples is heavy. Then, either
           either B1 or B2 is defective and light, or A3 is defective
           and heavy. So weigh B1 vs B2.

           Case 2.2.1 They balance. Then A3 is heavy.

           Case 2.2.2 B1 is lighter. Then it is defective and light.

           Case 2.2.3 B2 is lighter. Then it is defective and light.

   Case 3  A1, A2, B1, and B2 together BALANCE against A3, B3, and two C's.

           Then, either A4 is heavy or B4 is light. So just weigh A4
           against one of the C's. If it is heavy, it is the defective
           apple. If it balances, then B4 is the defective (light) one.

That was fun.
But your Logic Czar has no delusions of genius, have no fears.

Now back to our regularly scheduled arguments.

Jamie
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU