GPS and 8 Battery Puzzle

You have a GPS 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 GPS on.

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SherlockHolmes Expert Asked on 30th October 2019 in Math Puzzles.
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  • 2 Answer(s)

    Best solution I found so far will succeed in 8 attempts.

    Let’s call the batteries A, B, C, D, E, F, G and H.

    Attempt 1 : A & B
    Attempt 2 : C & D
    Attempt 3 : E &F
    Attempt 4 : G & H

    If no attempt has worked so far, it means that none of the pairs we tried contains 2 good batteries. And because we know that there are 4 good batteries and 4 bad batteries, that also means that none of the pairs contains 2 bad batteries. Each of the 4 pairs contains 1 good battery and 1 bad battery. If we focus on the two first pairs, that means that either A or B is good and that either C or D is good. Because of that, one of the 4 following attempts is guaranteed to succeed :

    Attempt 5 : A & C
    Attempt 6 : A & D
    Attempt 7 : B & C
    Attempt 8 : B & D

    stacil Curious Answered 4 days ago.

    You are absolutely right

    4 days ago.
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    There are 28 possible battery pairs (8×7/2).
    Only 6 of them have two working batteries (4×3/2)
    Worst case the first 22 pairs tried contain at least one wrong battery.
    So attempt 23 will succeed.

    CugelTheWise Expert Answered on 30th October 2019.
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