Math problem: Take some numbers from 50 numbers from 1 to 50, so that the sum of any two numbers cannot be divisible by 7. What is the maximum quantity?

Of the 50 numbers from 1 to 50,

Eight (1, 8, 15, 22, 29, 36, 43, 50) divided by 7.

There are 7 divisible by 7, and 7 divisible by 7 are 2, 3, 4, 5 and 6 respectively.

Out of the number:

If there is a number divisible by 7, 1, there can be no numbers divisible by 7 and 6 (all numbers can exist except those divisible by 7 and 6).

The number divided by 7 by 2 cannot have the number divided by 7 by 5 (all numbers can have it except the number divided by 7 by 5).

Numbers divided by 7 and 3 cannot have numbers divided by 7 and 4 (all numbers can have them except those divided by 7 and 4).

……

If there is a number divisible by 7, there can be no second number divisible by 7 (there can be any number except the number divisible by 7).

So take some numbers from the 50 numbers from 1 to 50, so that the sum of any two numbers cannot be divisible by 7.

The maximum number is 8+7+7+ 1=23.

Example: take 1, 8, 15, 22, 29, 36, 43, 50-4, 1 1, 18, 25, 32, 39, 46-.