Question

The sum of 6 consecutive integers is 204. what is the fourth number in this sequence?

Answer 1

Let
`x` by the smallest of the 6 integers. Then

`x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=204`

`\implies6x+15=204`

`\implies6x=189`

But 189 is odd, so it cannot be divisible by 6, which means
`x` is not an integer...