There Are 8 Batteries And Only 4 of Them Work - Google 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?
Guys do post explanations with your answers
It is a bit involved explanation, which I shall post later.
In my opinion, in the worst case it will need 8 Trials to guarantee success.
Minimum 1 trial and maximum 4 trails are required
Assumption: The individuals cells cannot be checked. The only way is to put them in the gadget in pairs and check whether the equipment comes on.
Procedure: Label the cells A-B-C-D-E-F-G-H. A good cell is given a value 1 and a dud one 0.
Divde the cells into pairs, A-B, C-D, E-F, and G-H to start with. The value of the four pairs has to be one of the following:
1. (A-B):(C-D):(E-F):(G-H) = (0,0):(0,0):(1-1):(1-1)
2. (A-B):(C-D):(E-F):(G-H) = (0:0):(1-0 OR 0-1):((1-0 OR 0-1):(1,1) and lastly
3. (A-B):(C-D):(E-F):(G-H) = (1-0 OR 0-1):(1-0 OR 0-1):(1-0 OR 0-1):(1-0 OR 0-1)
We start with loading the cells into the gadget one pair at a time and checking for functioning.
For option 1 above, the worst case will be: The first two can fail but the third pair must work.
For option 2 above, the worst case will be: The first three can fail but the fourth pair must work.
For option 3 above, all four pairs will fail. Take any two pairs, say A-B and C-D. These can form maximum four combinations:
(A-C):(A-D):(B-C):(B-D) having values (0-0): (1-0 OR 0-1): (1-0 OR 0-1):(1-1)
Try these pairs one at a time.
The worst case will be: The first three can fail but the fourth pair must work.
So without any prior knowledge of the status of each cell, we need a minimum of 8 trials to guarantee success.
If one is lucky, the very first pair can work, but no guarantee!
Total pairs that can be formed=8c2=28 pairs
There are three cases possible...
1.both not working= 4c2=6
2.1 working and 1 not working=4c1.4c1=16
So finally ,min trails=1
I am wrong. 8 is not the answer.