BdMO National 2013: Junior 7

[BdMO]

A positive integer is called “Fantabulous” if there is another fantabulous positive integer smaller than it. Find the number of fantabulous integers.

[shahriarabdullah]

Let $x$ be the smallest Fantabulous number. Due to condition we know that it is a positive integer. The smallest positive integer is $1$. So $x=1$. All other Fantabulous numbers will be valid if $1$ is a valid Fantabulous number. But there is no smaller positive integers than $1$. So $1=x$ can not be a Fantabulous number. So there are no valid Fantabulous numbers at all. Ans=0
Abdullah Shahriar