'let s be a collection of 16 integers, each from 1 to 30 inclusive. show that there must exist two distinct elements in s which differ by exactly 3. 'let s be a collection of 16 integers, each from 1 to 30 inclusive. show that there must exist two distinct elements in s which differ by exactly 3.
Any set with fewer than or more than 20 distinct elements cannot represent the set of integers from 1 to 20.
Integers are whole numbers, positive, negative or zero. Distinct merely means different.
The set of positive integers is {1,2,3,4,5,...}. When referring to numbers, distinct simply means different from each other e.g. 2,6,7 and 9 are distinct positive integers but 2,6,6 and 9 are not distinct since two of them are equal.
The sum of the integers from 1 to 100 inclusive is 5,050.
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
There are 22 integers between them.
The sum of all integers from 1 to 20 inclusive is 210.
The sum of the positive integers from 1,000 to 1,100 inclusive is: 106,050
To be pedantic, it is not.
2550
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