# GPS and 8 Battery Puzzle

95.6K Views

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

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.

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.

• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
• ### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
• ### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
• ### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
• ### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
• ### Five greedy pirates and gold coin distribution Puzzle

Five  puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
• ### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
• ### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
• ### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
• ### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
• ### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for \$10. It turned out ...Read More »
• ### Which letter replaces the question mark

Which letter replaces the question markRead More »
• ### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
• ### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
• ### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
• ### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
• ### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »
• ### Maths Genious Riddle

If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »
• ### Calling 2 as 10 Riddle

When do we call “10” while looking at number “2”?Read More »