Ans: 462
Not necessarily. Consider 444. The digits are not different. The first and second digits are not multiples of 3 The first digit is not greater than the second digit. In spite of all that, 444 is a 3-digit number
There are a lot of possibilities. The second digit can be 2 through 6, the third digit can be 3 through 7 as long as it is larger than the second digit. What we have so far: 1 _ _ 89
Since there is no whole part, compare the digits after the decimal point one by one (first digit with first digit, second digit with second digit, etc.), until you find two digits that are different.
There are the digits 1 through 9 for the first digit. Then, we have 0 through 9 for the second digit - excluding the first digit. For the third digit, we have 0 through 9 excluding the two previous digits
The first and last, and the second and third.
The first digit can be 0 through 9, ten possibilities. Having selected the first digit, you have 9 digits to pick from the second digit. Having selected the second digit, you have 8 digits to pick from the third digit. Hence total possibilities = 10 x 9 x 8 = 720
-- Calculate the square root in the usual fashion, continuing until you have two digits after the decimal point. -- If the second digit after the point is 4 or less, discard it, and what's left is your answer. -- If the second digit after the point is 5 or more, discard it, and increase the first digit after the point by '1' to get your answer.
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
1155
There are 90 palindromes with 4 digits.The first digit can be any digit from the set {1,2,3,4,5,6,7,8,9}.With each choice of the first digit, the second can be any digit from the set {0,1,2,3,4,5,6,7,8,9}.That makes 9*10 = 90 permutations for the first two digits. These determine the palindrome since the third and fourth digits are the same as the second and first, respectively.
Just compare the digits one by one: compare the first digit after the decimal point with the first digit of the other number, the second digit with the second digit, etc., until you find a digit that is different.
89