Question

How many alphabets needed to be there in a language if one word to make 1 million distinct 3 digit initials using the alphabets of the language?

Answer 1

1 million distinct 3 digit initials are needed.

Let the number of required alphabets in the language be ‘n’.

Therefore, using ‘n’ alphabets we can form n * n * n = n3n3 distinct 3 digit initials.

Note distinct initials is different from initials where the digits are different.

For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.

This n3n3 different initials = 1 million

i.e. n3=106n3=106  (1 million = 106106)

 => n = 102102 = 100

Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.