There are `n` locks and `n` matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trails required to open a lock.

A number lock can be unlocked by a 3 digit code, each digit of the code could be any one of 0, 1 ....,9. What is the maximum number of trials required to unlock, if the following are known (a) the last digit (b) the sum of the first two digits is always less than or equal to the third?

The lock of a safe has a dial with holes, sasy ten, in which the numbers 0,1,2,……..9 are inscribed in each hole. The lock can be opened only when a specific code numbersay of six digits is dialled. Suppose the code number is 249916, it means that the can be opened when we first dial 2, then 4 nd so on. Find the maximum number of trials which do not result in opening the lock.

If each match box contains 50 matchsticks , the number of matchsticks required to fill n such boxes is

Who proposed the lock and key hypothesis ?

The chest is locked by a number of padlocks. All padlocks must be unlocked in order to open the chest. 12 Copies of the keys to the padlocks are distributed lie next to it, such that any group of 7 or more keys can open the chest should they choose to do so, but any group of less than 7 cannot. What is the minimal number of padlocks required to achieve this?

If N={a,b,c,..z} then find the number of all possible subsets of N.