Fifty
279,999,720
First, separate the negative and positive integers (put them into two separate groups). If there is a zero, you can put it in its own group - or put it into the same group with the positive integers. Negative integers come first, then zero, then positive integers.For positive integers:An integer with less digits comes before an integer with more digits.For integers with the same number of digits, look at the first digit. The integer with the smaller digit in this position comes first.If the first digit is the same, look at the second digit. If those are equal, look at the third digit, etc.For negative integers, it is the other way round - for example, an integer with MORE digits comes first.
Positive integers are greater than negative integers. For positive integers: * The integer with more digits is larger. * If two integers have the same length, compare the first digit. If the first digit is the same, compare the second digit, then the third, etc., until you find a difference. In each case, the integer with the larger digit (at the first position where you find a difference) is the larger one.
All the numbers from 10 to 99 are positive 2 digit integers
There are 320 such numbers.
Three of them.
279,999,720
20. 16 without repeating a digit.
First, separate the negative and positive integers (put them into two separate groups). If there is a zero, you can put it in its own group - or put it into the same group with the positive integers. Negative integers come first, then zero, then positive integers.For positive integers:An integer with less digits comes before an integer with more digits.For integers with the same number of digits, look at the first digit. The integer with the smaller digit in this position comes first.If the first digit is the same, look at the second digit. If those are equal, look at the third digit, etc.For negative integers, it is the other way round - for example, an integer with MORE digits comes first.
Positive integers are greater than negative integers. For positive integers: * The integer with more digits is larger. * If two integers have the same length, compare the first digit. If the first digit is the same, compare the second digit, then the third, etc., until you find a difference. In each case, the integer with the larger digit (at the first position where you find a difference) is the larger one.
All the numbers from 10 to 99 are positive 2 digit integers
To find the number of three-digit positive integers with digits whose product is 24, we can break down 24 into its prime factors: 2 x 2 x 2 x 3. The possible combinations for the three digits are (2, 2, 6), (2, 3, 4), and (2, 4, 3). These can be arranged in 3! ways each, giving a total of 3 x 3! = 18 three-digit positive integers.
There are 320 such numbers.
18 positive integers and 36 integers (negative and positive)
-23
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.
4 digits - representing 16 integers.