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...