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### Logic Puzzle Question

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 ?

1. To get the flashlight on ,one needs 2 good batteries.
The 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)

1. Absolutely right.

- S Kumar

2. Dividing 3+3+2 is fine.
And if U start trying with the group of 2 batteries first, only 6 trials are enough. It is also the worst case analysis.

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

3. to GUARANTEE, 19

4. it 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.........

5. 7
You 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.

6. Dividing 3+3+2 is fine.
And if U start trying with the group of 2 batteries first, only 6 trials are enough. It is also the worst case analysis.

7. Try 4 pairs and it fails to light.
Then exchange batteries from 2 pairs
One will work and other wont.
Then exchange batteries from other 2 pairs.
U get in 8 attempts