Debbie has a lot more apples to check. Now she has five apples. four apples are

Question

Debbie has a lot more apples to check. Now she has five apples. four apples are good, all weighing the same. But the bad one either weighs more or weighs less than the others. List the process steps and decision you need to make in order to determine which apple is bad, and whether it is heavier or lighter than the good ones. You know one of the apples is either heavier or lighter than all the others, what are the minimum weighs needed to determine which apple is bad, and whether it is heavier or lighter than the others. Show and justify your solution.

Explanation / Answer

You need at least 4 weighs to find the bad apple, and to know whether it is heavier or lighter.

For the first weigh, put apples A, B on one side of the balance and C, D on the other side of the balance. If they balance, then apple E is bad and use another weighing to determine whether it is heavier or lighter. If not, proceed to the second weigh.

For the second weigh, replace apple D with apple E. If they balance, apple D is bad and use another weighing to determine whether it is heavier or lighter. If not, one of apples A, B, C is bad.

For the third weigh, put apple A on one side and apple B on the other side. If they balance, then apple C is bad and use another weighing to determine whether it is heavier or lighter. If not, proceed to the next weigh.

For the fourth weigh, replace apple B with apple C. If they balance, apple B is bad and you can know whether it is heavier or lighter from the third weigh. If not, apple A is bad and you can know whether it is heavier or lighter from the fourth weigh.

Hope my explanation helps.

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