Ken's blog

On a late June afternoon, Jill sat on the green grass by a small lake at the university with a concentrated look on her face. Some ducks were quacking nearby.

“Hi Jill, I see you are thinking about something, anything important?” said Jack, who had quietly walked up to her on the grass.

“I need a vacation and there’s this problem I’m trying to work out, Jack” said Jill in an exasperated tone of voice.

“Seems you are not progressing much. Tell me all about it,” said Jack, sitting down beside her.

“The travel magazine ‘Your Perfect Vacation’ is holding a contest where the winner will get a two week, fully paid vacation for two at a bungalow in Curacao in the Caribbean, and I want to win the prize,” she said with a determined look.

“Sounds interesting. I enjoy basking in the sun and doing some snorkeling. Want some company on the trip if I help you?” offered Jack eagerly.

“You bet, Jack. Have a look at the problem, the deadline is tomorrow.” Jill handed him the magazine, pointing to the advertisement.

Jack began reading out loud: “There is a number that starts with a digit and is followed by four digits that are the same. Square this number and subtract one to give a ten digit number, none of whose digits are the same.”

Jill was looking expectantly at him, hoping to see a light turn on in his eyes.

Jack’s face brightened up. “Jill, this is no big problem. Some number theory that I know will make it easy,” smiled Jack.

“So glad to hear it, Jack. Let’s go over to my place, work it out and enter the solution on the magazine’s webpage,“ invited Jill.

“Curacao, here we come,” said Jack, nimbly pulling Jill up on her feet.

Jack and Jill gathered their things and walked off together down a tree-lined path.

What do you figure is the number Jack and Jill are looking for?