You have a flashlight and 8 batteries

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Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

Answer: 7. If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.

Riddle Discussion

By: 0wewewe0 on 13/9/14

7. Let's name batteries ABCDEFGH. First let's test AB, CD, EF, GH (4 tests). in worst possible case neither on those pairs will work but we now know for sure that each pair has at least one working battery. Now we take AB and CD and try different combinations of them : AC, BC, AD, BD. In worst possible case the first three(3 tests) dont work and now we know for sure that the forth must work.
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