AA Batteries
Probability
Level
pending
You have a flashlight that takes 2 AA working batteries. You have 8 AA batteries but only 4 of the AA batteries actually work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
2
7
4
1
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1 solution
If you place the batteries into 3 groups: there will be 2 groups of 3 and one group of 2. By doing this, you will mainly guarantee that one of the groups has 2 AA batteries that are actually working. Both of the groups of 3 have 3 possible combinations of 2 AA batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find 2 AA batteries that work.