The sum of the even numbers is (26 + 28 + ... + 100); The sum of the odd numbers is (25 + 27 + ... + 99) Their difference is: (26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99) = 1 + 1 + ... + 1 There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38. So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.
Between them, not including them it is 36. If you include these two numbers, it would be 38.
Square numbers, like 49, have an odd number of factors.
29 31 37.
The parity rules are: Odd + Odd = Even Even + Even = Even Odd + Even = Odd Even + Odd = Odd So the parity where one number is even is that of the other number. This means that you can go through a list of numbers and ignore all the even numbers. Every PAIR of odd numbers has even parity and by the previous paragraph, even parity can be ignored. So you can pair off odd numbers and ignore them.
The number of odd numbers between 38 and n = int[abs(n - 38)/2]
38
38 of them.
The sum of the even numbers is (26 + 28 + ... + 100); The sum of the odd numbers is (25 + 27 + ... + 99) Their difference is: (26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99) = 1 + 1 + ... + 1 There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38. So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.
The terms "even" and "odd" apply to whole numbers, not to decimals or fractions.
Between them, not including them it is 36. If you include these two numbers, it would be 38.
Square numbers, like 49, have an odd number of factors.
There are 3 composite numbers between 35 and 40. They are 36, 38, and 39.
29 31 37.
"Two consecutive numbers" implies that these are whole numbers. Consecutive whole numbers have different parity - that is to say that one is odd and the other even, which means that their sum must be odd. Since 38 is even the problem has no solution.
The parity rules are: Odd + Odd = Even Even + Even = Even Odd + Even = Odd Even + Odd = Odd So the parity where one number is even is that of the other number. This means that you can go through a list of numbers and ignore all the even numbers. Every PAIR of odd numbers has even parity and by the previous paragraph, even parity can be ignored. So you can pair off odd numbers and ignore them.
None that are all odd numbers. But, there are two sets of three consecutive numbers containing a mix of even/odd that add up to 120. They are 39, 40 and 41 and also 38, 40 and 42.