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Unformatted text preview: Now we deal with the case in which the scale does not balance. Ill assume the balls are labeled so that one of the balls 9, 10, 11, 12 is heavy or one of the balls 5, 6, 7, 8 is light. Place balls 5, 9, 10 on one side and balls 6, 11, 12 on the other. If the scale balances, ball 7 or 8 must be bad and it must be light. Weighing them against each other will figure it out. So we can suppose they dont balance, and that the balls are labeled so that the pan with the balls 6, 11, 12 is heavier than the pan with the balls 5, 9, 10. This allows us to conclude that one of ball 11 or 12 is heavy or ball 5 is light  this follows because the bad ball cannot be on the light side of the scale for the first weighing and the heavy side of the scale for the second weighing. For the last weighing, put balls 5, 11 on one side and two good balls, say 1,2, on the other. Knowing that 5 is light or that 11 or 12 is heavy will allow you to conculde which ball is bad....
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This note was uploaded on 03/01/2010 for the course MATH 301 taught by Professor Albertodelgado during the Spring '10 term at Bradley.
 Spring '10
 AlbertoDelgado
 Combinatorics

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