**Logic Puzzle Question - 10 November**

You are camping with your friends. You have a flashlight for any emergency and have brought 8 batteries along with you. Your brother calls to tell you that four of those batteries are already dead.

Your flashlight requires two working batteries to run. What is the least number of pairs you will need to test to guarantee that you can get the flashlight on ?

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ReplyDelete1

ReplyDelete9

ReplyDelete24

DeleteTo get the flashlight on ,one needs 2 good batteries.

ReplyDeleteThe optimal way (less trials) is to divide randomly the 8 bat. in 2 groups of 3 ,and 1 group of 2 batteries.

Then, according to a famous and very useful mathematical principle called "Pigeonhole Principle", one of the three groups will always have 2 good batteries.

Each triplet has c(3,2)=3!/(1!*2!)=3 combinations

If the two good ones are in the only couple= 1 combination.

So, maximal no. of tests:

3+3+1=7 (if we are lucky,we will do it in less tests)

brilliant!!

DeleteAbsolutely right.

Delete- S Kumar

Dividing 3+3+2 is fine.

DeleteAnd if U start trying with the group of 2 batteries first, only 6 trials are enough. It is also the worst case analysis.

least number is 1 (you were lucky and got them to work without changing)

ReplyDeleteto GUARANTEE, 19

ReplyDeleteit is 8.....make four pairs and test...in worst case scenario all pair will have 1 faulty........take any two pairs...each will have one fault......at max on 4 run you can tell which two are good one.........

ReplyDelete7

ReplyDeleteYou must first divide the batteries in three groups: a group of two batteries and two groups of three batteries each. Now you have made sure that one of the group has two working batteries.

Now both the groups with three batteries can form three possible combinations and the group with two batteries has just one combination.

3 + 3 + 1 = 7.

Dividing 3+3+2 is fine.

ReplyDeleteAnd if U start trying with the group of 2 batteries first, only 6 trials are enough. It is also the worst case analysis.

Try 4 pairs and it fails to light.

ReplyDeleteThen exchange batteries from 2 pairs

One will work and other wont.

Then exchange batteries from other 2 pairs.

U get in 8 attempts