In the 100 natural numbers from 1 to 100, take two different numbers and add them together. The sum is a multiple of 3. There are () different methods

These 100 numbers can be divided into 1,4,7.. 2,5,8.. 3,6,9
That is, there are 34 3K + 1, 33 3K + 2 and 33 3K + 3
Take out two numbers, two ① is 6K + 2 does not match
Two ② are 6K + 4 inconsistent, two ③ 6K + 6 consistent
① + 2 = 6K + 3 in accordance with, 1, 3, 2, 3 not in accordance with
There are 2 species, 3 species, 1 + 2 species
There are 66 kinds in total. The main problem is to separate 3K + 1, 3K + 2 and 3K + 3

How many methods are there to add two different books out of the 100 natural numbers from 1 to 100, whose sum is a multiple of 3?
As long as the final result of a total of several on the line! Is not a book number

There are 1650 kinds of answers. The sum of 1 and 3 is a multiple of 2, 5, 8 98. There are 33. The sum of 2 is a multiple of 3. There are 4, 7, 10 There are 33 numbers in total. The sum of 3 is a multiple of 3. There are 6, 9, 12 99. There are 32. The sum of 4 is a multiple of 3. There are 5, 8, 11 98. Total 32. And 5

At 1, 2, 3 Of the 2000 natural numbers, there are______ Natural numbers can be divisible by 2 and 3 at the same time, and cannot be divisible by 5

The number that can be divisible by 2 and 3 at the same time, that is, the number that can be divisible by 6 is 1, 2, 3 There are 6, 12, 18, 24 Let there be n such numbers, then: 1998 = 6 + (n-1) × 6, n = 333. Therefore, there are 333 numbers divisible by 2 and 3 at the same time. Among these 333 numbers, 30, 60, 90, 120 Suppose there are m such numbers, then 1980 = 30 + (m-1) × 30, M = 66, that is, there are 66 numbers divisible by 5. Therefore, there are 333-66 numbers divisible by 2 and 3 at the same time, and there are 267 numbers divisible by 5

In natural numbers, 1,2,3,..., 100, how many numbers are multiples of 2 and 3, but not multiples of 5?

A multiple of two and three is a multiple of six
100 / 6 = 16.666
But it's either a multiple of 5 or a multiple of 30, 100 / 30 = 3.333
16-3 = 13

In the 100 natural numbers from 1 to 100, take two different numbers and add them together. The sum is a multiple of 3. There are () different methods