Find the number of positive numbers less than 2020, which can not be written as the sum of six consecutive positive numbers.

Answer: 334

Step-by-step explanation:

6 consecutive numbers can be written as:

n, n+1, n+2, n + 3, n + 4, n + 5,

The addition of those 6 numbers is:

n + n+1 + n+2 + n + 3 + n + 4 + n + 5

6n + 1 + 2 + 3 + 4 + 5 = 6n + 15

Let's find the maximum n possible:

6n + 15 = 2020

6n = 2020 - 15 = 2005

n = 2005/6 = 334.16

The fact that n is a rational number means that 2020 is can not be constructed by adding six consecutive numbers, but we know that with n = 334 we can find a number that is smaller than 2020, and with n = 335 we can found a number bigger than 2020.

So with n = 334 we can find one smaller.

6*334 + 15 = 2019

and we can do this for all the values of n between 1 and 334, this means that we have 334 numbers less than 2020 that can be written as a sum of six consecutive positive numbers.