"I've asked you to tell me independently each a 4-digit number and after a while, I'm happy to announce that if any of you will divide their number by mine you will end up with the same remainder! "

Now that you know it I'm sure that you will be able jointly to figure the value of my number...- of course it will be the largest of the qualifying candidate answers...

Adam: It could not be true for any three non-related 4-digit numbers!

Betty: You were extremely lucky to find such a special number!

Dan: And now we will be able to calculate the value of your number!

Indeed, Adam(2479), Betty(6181), and Dan(8649), after a not-so-long brainstorming session successfully restored Jerry's number.

a. What was it?

b. d4 bonus question:

What's the probability of Jerry "success" with 3 **RANDOMLY CHOSEN**

three 4-digits numbers.

Provide your estimate, listing your assumptions and reasoning.