Can $18$ consecutive positive integers be separated into two groups, such that their product is equal? We cannot leave out any number and neither we can take any number more than once.
When the smallest number is not $17$ or its multiple, there cannot exist any such arrangement as $17$ is a prime.
When the smallest number is a multiple of $17$ but not of $13$ or $11$, then no such arrangement exists.
But what happens, when the smallest number is a multiple of $17$ and $13$ or $11$ or both?