How many numbers we can create using $1,2,3,4$ when repetition is allowed?

Question

How many numbers we can create using $1,2,3,4$ when repetition is allowed?

Condition: The number must have at most 5 digits.

My Attempt :

5 Digit number of numbers: $4\times4\times4\times4\times4 =1024$

4 Digit number of numbers : $4\times4\times4\times4 =256$

3 Digit number of numbers : $4\times4\times4 =64$

2 Digit number of numbers : $4\times4 =16$

1 Digit number of numbers: $4 =4$

Am I missing something? The answer given is $3125$

Answer 1

The answer depends on whether you're looking for strings or numbers. Take max 2 digits for example,

1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34,41,42,43,44 -> 4+4^2 = 20 numbers

__,_1,_2,_3,_4,1_,2_,3_,4_,11,12... -> 5^2 = 25 strings, where _ is to represent empty string.