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 = n3 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 n3 different initials = 1 million
======>>>>> i.e. n3 = 106 (1 million = 106)
======>>>>> n3 = (102)3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.