Take any 27 natural numbers from 1-50 nature books, and two of them must have a sum of 52. Why?

Take any 27 natural numbers from 1-50 nature books, and two of them must have a sum of 52. Why?

If the sum of two numbers obtained is not 52, group 50 numbers, and the sum of two numbers in each group is 52 (50,2) (49,3) (48,4) (47,5) (46,6) （28,24）（27, 25) the sum of any number in the range of 26 and 1 is not 52. If you want the sum of two numbers not 52, you can only take one number in each group. There are 50-27 + 1 = 24 groups in total. If you take 26 and 1 again, the sum of each number will not be 52. If you take the 27th number, you must add it to a number in group 24 to get 52, so you can take any 27 numbers from 1 to 50, The sum of two numbers must be equal to 52

A positive integer is equal to 150 of the sum of all the natural numbers in front of itself. The natural number is______ ．

If the natural number is one digit, it is impossible. If the two digit is set as 10A + B, then according to the meaning of the title, 10a + B = 50 (a + b), simplify 40A + 49b = 0, and there is no positive integer solution. If the three digit is set as 100A + 10B + C, then according to the meaning of the title, 100A + 10B + C = 50 (a + B + C), simplify 50A = 40B + 49C, because 40B + 49C ≤ 40 × 9 + 49 × 9 = 801, a = 4, B = 5, this number is 450. If this number is more than four digits, there is no integer satisfying the condition, so the answer is 450

What's one in 23 out of 3

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