Mindbender

A: Andy slammed the letter down on his desk angrily. "Still no payment on my claim," he said. "Now they want the serial number."

"Do you have a note of it?" asked Mary.

"Of course, but I'll give it this way." Her husband chuckled. "It's just one less than twice the square of its last three digits."

What was the number?

B: "What was that number?" asked Susan. "I forgot to write it down."

"You did? Then work it out yourself," replied Andy. "It's 17 more than one perfect square, but 6 less than another perfect square."

You try!