Alex Y
The key here is to find the most efficient way to get info by testing subsets of the eight batteries. For instance, in the (sub-optimal) solution shown before, the batteries were separated into 4 pairs, and testing the pairs told us that each pair had one good battery, and from there, it was just three more tests before knowing that we will light the flashlight with the eighth pair we install.

Another way to get a good pair installed no later than the 8th pair (and identified after the 7th failed test) is to divide the batteries into two groups of 4. Test the 6 pairings of 1-4, and if those do not light the flashlight, you know there is at most one good battery in 1-4, so at least 3 good batteries in 5-8. Pick any pair of 5-8, and if it fails, the other two batteries will light the flashlight.

But there is a grouping that will assure that you can light the flashlight with the seventh pair you try.

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