100 Batteries

Probability Level 3

You go into your garage and find a pile of 100 batteries (all the same type).

You happen to know that half of them are good and half are bad, but you can't tell which is which.

You have a flashlight which uses two batteries, and requires both to work in order to turn on.

In the worst case scenario, with an optimal strategy, what is the minimum number of times you will need to put batteries into the flashlight before you can guarantee to get a working pair in the flashlight?

Details and Assumptions:

  • The flashlight either turns on or it doesn't, i.e. there is no way to distinguish between one of the two working and neither one working.

  • Your answer should be the number of "flashlight loadings" you will need to actually get your flashlight working, not just how many you would need to identify two good batteries.

Image credit: https://www.slrlounge.com

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