For single digit numbers in the range 0-9 there are 4 (excludes zero).
For 2 digit numbers in the range 10-99, then the even sum condition only applies when both digits are even, i.e. such numbers ending in 0,2,4,6,8 in the 20s, 40s, 60s & 80s. There are 4 x 5 = 20.
For 3 digit numbers in the range 100-999 then the even sum condition applies when (1) All 3 digits are even or (2) The first 2 digits are odd and the third digit is even.
(1) There are 4 options for the 1st digit (2,4,6,8), and 5 options for the 2nd and 3rd digits (0,2,4,6,8) There are thus 4 x 5 x 5 = 100 qualifying numbers.
(2) If the 1st and 2nd digits are odd and the 3rd digit is even then there are 5 x 5 x 5 = 125 qualifying numbers.
Total number of qualifying numbers = 4 + 20 + 100 + 125 = 249
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
There are 3168 such numbers.
750
Infinitely many, since every positive number is a square of some other number. However, there are 21 perfect squares (SQUARES OF INTEGERS). From 112 to 312, inclusive.
332
The sum of the positive integers from 1,000 to 1,100 inclusive is: 106,050
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
There are 3168 such numbers.
There are 200 positive four digit integers that have 1 as their first digit and 2 or 5 as their last digit. There are 9000 positive four digit numbers, 1000 through 9999. 1000 of them have 1 as the first digit, 1000 through 1999. 200 of them have 2 or 5 as their last digit, 1002, 1005, 1012, 1015, ... 1992, and 1995.
All multiples of 3 have digits that add up to a multiple of 3. There are 333 multiples of 3 between 1 and 1000.
from 1000 to 9999, ie 9999 - 999 = 9000
All multiples of 3 have digits that add up to a multiple of 3. There are 333 multiples of 3 between 1 and 1000.
There are one thousand. Starting at 2000 and going to 2999
The sum of the squares of the first 1000 positive odd integers (from 12 to 19992) is 1333333000.
From 1000 to 9999 (inclusive) there are 9999 - 1000 + 1 = 9000 integers. Half of which are even, half of which are odd. So the answer is 9000/2 = 4,500.
To determine the number of positive integers less than 1000 with distinct digits and are even, we need to consider the possible combinations of digits. Since the number must be even, the last digit must be even, giving us 5 options (0, 2, 4, 6, 8). For the hundreds digit, we have 9 options (1-9), and for the tens digit, we have 8 options (0-9 excluding the hundreds digit and the last digit). Therefore, the total number of such integers is 5 * 9 * 8 = 360.
750