Find The right cell

Logic Level 3

You are given a torch and 6 cells. The torch runs on 3 charged cells. Out of the given 6 cells, 3 cells are charged and other 3 are uncharged but you don't know which one is charged and which one is uncharged. What is the least number of attempts you need to make, to ensure it will light up the torch ?

13 16 12 20 14 8 15

2 solutions

Shikhar Srivastava
Apr 12, 2020

There are 3 charged cells out of 6 cells given and we have to get that all the charged cells since there is no option of leaving any charged cells means there are no more than the required number of charged cells, we have to attempt all the combination of selecting 3 cells at a time and considering the worst case the last selection will lit the torch. So the answer is $\binom {6}{3} = 20$

In fact I believe that if there are $n$ cells given and $m \leq n$ cells are charged and the torch uses $m$ cells to light up then the least number of attempts to lit the torch is $\binom {n}{m}$ . I don't know whether this hypothesis is true or not. If it is true I am not able to prove it.

Kano Boom
Apr 7, 2020

6C3 = 20 different possible combinations

will your method work if there are 8 cells out of which only 4 are charged and a torch which runs on 3 cells. According to your method total number of combination is $\binom {8}{3} = 56$ and number of possible combination of charged cell is $\binom {4}{3} = 4$ . So assuming the worst case 56 - 4 + 1 = 53 will be your answer. But I don't think that 53 is the least number of attempt to lit the torch.

Shikhar Srivastava - 1 year, 2 months ago

Not sure...

Kano Boom - 1 year, 2 months ago

Find The right cell

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