The number of 3-digit numbers in all in the base-10 system is

The difference of the number of 4 digit numbers and the number of 3 digit numbers in base 10 system is

How many three-digit numbers in base 10 are three-digit numbers in base 8 but not in base 7?

In decimal system there are 10 digits 0, 1, 2, 3, . . . till 9. Similarly, there is a system which has only 3 digits 0, 1 and 2. Numbers represented in such systems are called base 3 or trinary numbers. A = 389 + 1  is a number in the decimal system. B is the trinaryequivalent of this number. How many zeros are there in B ?

A number in a base is said to be a special number if it is equal to the sum of its own digits each raised to the power of the number of digits. A number in base ‘b’ can have digits from 0 to b-1. By default the numbers used by humans is to base 10 and called as decimal number system. A number ‘n’ from decimal number system can be converted to any base ‘b’ by repeated division of ‘n’ by ‘b’ and writing reminder of each division in reverse order. For example, number 24 is converted to base 3 as shown below:

The smallest two-digit number that is not the sum of three different one-digit numbers is