I recently attended a test which ask me two question based on perfect squares; here they are:
$1.$ How many even perfect squares between $1000$ and $5000$ are divisible by both $5$ and $9$?
$2.$ Can there be a perfect square whose digits consists of exactly $4$ ones, $4$ twos and $4$ zeroes in any order?
I haven't done anything much on perfect squares so I was reluctant to attempt them during exams, although as I had some spare time after finishing the other questions, I tried thinking about the first problem and I noticed that only $3600$ seems to satisfy the conditions, which is correct, but I don't know how to get this mathematically? And for the second problem, I don't have any clue till now.
Unfortunately they haven't given me any solutions for the questions, nor any ideas as to how to solve them (mathematically)?