In & nbsp; 1, 2, 3, 4 Take two numbers out of the 100 numbers, so that the sum of the two numbers can be divisible by 4, at most______ There are two different methods

In & nbsp; 1, 2, 3, 4 Take two numbers out of the 100 numbers, so that the sum of the two numbers can be divisible by 4, at most______ There are two different methods

These 100 numbers can be divided into four groups according to the remainder of division by 4: 0, 1, 2, 3. These four groups are the groups with the remainder of 0: 4, 8, 12 Group 1, 5, 9, 13 The group with the remainder of 2: 2, 6, 10, 14 The group with the remainder of 3: 3, 7, 11, 15 If the sum of any two numbers can be divisible by 4, it can be as follows: 1. Take any two numbers in the first group, there are C (25,2), that is, 25 × 242 × 1 = 300; 2. Take one number in the second and fourth groups, there are 25 × 25, that is, 25 × 25 = 625; 3. Take any two numbers in the third group, there are C (25,2), That is to say, 25 × 242 × 1 = 300 (species) and 300 + 625 + 300 = 1225 (species) at most