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Heavy Weight
(solution)
To identify the heavier weight in two weighings perform the following
sequence of moves as shown in the illustration.
First divide all the weights into three triplets. Weigh one triplet
against another - see Weighing 1 in the top left corner of the
illustration above. There can be three different results of the weighing
1 - phases 1A, 1B and 1C respectively (see the illustration).
If the result is phase 1A, then choose any two weights from the third
triplet and weigh one weight against another - this will be the second
weighing (phase 2A). If the result after the second weighing is phase 2AA then the
heavier weight is the one left from the third triplet. If the result is
either of the phases 2AB and 2AC, then the heavier weight is the one on
the lower pan.
If the result after the first weighing is either of the phases 1B and
1C, then choose any two weights from the triplet on the lower pan and
then weigh one weight against another - this will be the second
weighing (phases 2B and 2C respectively). If the result after the second weighing is phase 2BA (or 2CA
respectively) then the heavier weight is the one left from the
triplet taken from the lower pan after the first weighing. If the result
is either of the phases 2BB and 2BC (2CB and 2CC respectively), then the
heavier weight is the one on the lower pan. |
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