Question

If the maximum number of trials required to open all locks when there are 'n' locks and 'n' keys is 105. Find 'n'

Answer 1

Answer:

14

Step-by-step explanation:

total locks = n

first lock & first key = n trials

second lock & second key = n-1 trials

and so on ...

hence all trials = n+(n-1)+(n-2)+......105

Rearrange : 1+2+3.....n

n(n+1)/2 = 105

n(n+1) = 210 : (n^2+n-210=0)

n= 14

Note :

1)sum of N numbers : n(n+1)/2

1) solve the quadratic equation