Question

How many 4 digit numbers possible such that if 4 digit number is n then n^2 should contain n as lsb?

Answer 1

Answer:

The first (non-zero) digit of the number FF(thousands digit) can be any one of nine. The second digit SS which is used if there are two digits can be any one of the nine digits different from the first.

Now consider the Hundreds Tens and Units digits in the case that there are two digits used in the number. We have two possibilities FF or SS to fill each place - but we exclude FFFFFF as not involving two digits, so there are 23−1=723−1=7 possible patterns with exactly two different digits and 9×99×9 ways of choosing the pair of digits in the first place.

Then there are nine possibilities with just one digit.

So the total you want is 9×9×7+9=576