Natural number 1.2.3... 100, how many numbers can be taken out at most, so that the sum of any four numbers can be divided by 15 Is the correct answer 6,

First of all, we make sure that the sum of four numbers is a multiple of 15, such as 2, 3, 4, 6. If we take out a group of more than four numbers, the sum of one group of four numbers is a multiple of 15, and then exchange the other number with the number in the four, and the sum of the new four numbers is also a multiple of 15, which means that the sum of the two numbers exchanged is a multiple of 15

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1. The maximum number can be taken from natural number 1.2.3.100, so that the sum of any four numbers can be divided by 15 Speed! process
2. How many numbers can be taken out from the natural number 1,2,3,4,5... 100, so that any four of them can be divided by 15?
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