Problem - 4150
Let $N$ be a square number. If its units digit is $6$, then its tens digit must be odd.
Clearly, $N$ is even. Hence, $N$ must be a multiple of $4$. Then, it is easy to verify that its tens digit must be odd: $16$, $36$, $56$, $76$, and $96$ are all multiples of $4$. But none of $06$, $26$, $46$, $66$, and $86$ satisfies this requirement.