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.

SherlockHolmes Expert Asked on 30th October 2019 in Math Puzzles.
Add Comment

  • 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 on 12th November 2019.

    You are absolutely right

    on 13th November 2019.
    Add Comment

    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.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.
  • More puzzles to try-