In the 100 natural numbers 1.2.3... 100, take two different numbers so that their sum is a multiple of 7. How many different ways are there?

In the 100 natural numbers 1.2.3... 100, take two different numbers so that their sum is a multiple of 7. How many different ways are there?

The remainder of 100 numbers divided by 7 can be divided into seven categories as follows: the number of 7n-6 has 106 / 7 integers = 15, the number of 7n-5 has 105 / 7 integers = 15, the number of 7n-4 has 104 / 7 integers = 14, the number of 7n-3 has 103 / 7 integers = 14, the number of 7n-2 has 102 / 7 integers = 14, the number of 7n-1 has 101 / 7 integers = 14, the number of 7n has 100 / 7 integers = 14

In 1,2,3,4 Take any two different numbers from the 100 natural numbers, so that the sum of the two numbers is a multiple of 6. How many methods are there?
Northeast Yucai online question bank level 9 questions

These 100 numbers are divided into six categories: 1 divided by 6, there are 17; 2 divided by 6, there are 17; 3 divided by 6, there are 17, 6 divided by 4, there are 17, 6 divided by 5, there are 16, 6 divided by 5, there are 16. The sum of 1 divided by 6 and 5 divided by 6 can be divided by 6, there are 17 × 16 different methods

From 1, 2 How many ways are there to make the sum of these three numbers a multiple of 3?

Let a = {1, 4, 7, 10 ，28}，B={2，5，8，11，… ，29}，C={3，6，9，… There are three kinds of number sets, which have the following four types: 1. Take one number from a, B and C, and there are C101, C101, C101; 2. Take only three numbers from a, and there are C103; 3. Take only three numbers from B, and there are C103